Are you speaking about discrimination from Italian citiziens or from Italy's fascist government?

If you are speaking about the former, antisemitism wasn't a really a thing in Italy. Jews were pretty much accepted, and some jews like Ettore Ovazza were even members of the facist party.
From http://www.acjna.org/acjna/articles_detail.aspx?id=300

The Italian Jews, representing just 0.1 percent of the Italian population, were the most assimilated Jews in Europe. Although Italy is a nation with a strong Catholic tradition, Jews were accepted as important members of society and were successful in the military, politics, and in every skilled profession. When Benito Mussolini’s government asked the Italian people to turn on their neighbors, an astoundingly large number said “No.” As a result, a higher percentage of Italian Jews were saved than in any other occupied country, aside from Denmark. The Italian role in the Holocaust is a complicated one, with condemnable official behavior, but an impressive popular rejection of anti-Semitic policies.
Cecil Roth, author of “History of the Jews of Italy,” also described the nation as very accepting. “After 1870, there was no land in either hemisphere where conditions were or could be better. It was not only that disabilities were removed, as happened elsewhere too during these momentous years, but that the Jews were accepted freely, naturally and spontaneously as members of the Italian people, on a perfect footing of equality with their neighbors.”
[...]Italian Jews achieved a level of acceptance without parallel in any other country. While France was bitterly divided over the fate of Captain Dreyfus, Italian Jews were acting as generals, cabinet ministers and prime ministers.”

[...]Stille describes how widespread Jewish fascism was, “Although there are instances of Jews making compromises with fascism elsewhere in Europe, these were isolated cases of personal opportunism, of private pacts with the devil. In Italy, Jewish fascism was a real ideological movement, a mass phenomenon, as much as that was possible in Italy’s tiny Jewish population of 47,000. In 1938, at the beginning of the racial laws, more than 10,000 Jews-about one out of every three Jewish adults-were members of the Fascist Party.”

If you are instead asking about jewish persecution from the fascist government, there wasn't any until 1938, then in 5 august "La difesa della Razza" (in defence of the race) magazine was published by the fascist party, and declared that a pure Italian race existed, and that jews weren't part of it.

From september 1938 Jew couldn't be teachers anymore. From october they couldn't be member of the fascist party, of the military, and they couldn't own companies with more of 100 employees. In november all jews were fired from all public institutions. From 1939 they couldn't be journalist, then in 1940 Mussolini stated that all Italian jews had to be expelled within 10 years.

There weren't any extermination camps in Italy, and until 1943 non Italian or "dangerous" Jews were simply arrested and put into interment camps, just like other antifascists. Only in 1943, with the nazi invasion, all Jews were declared strangers and part of an enemy nation, and only then jews started to be deported to extermination camps.

The question of Italian Fascism's antisemitism is one of the more debatable subjects in Italian historiography. While Mussolini's regime passed various antisemitic laws and restrictions in the 1930s, this state-sponsored antisemitism was seldom connected to popular violence and ritualistic humiliation like in Germany. Nor were there many prominent advocates of biological antisemitism within Italian Fascism. There were a few Fascist intellectuals that argued Italian Jews were a species apart from the Italian race, but most Fascist antisemites tended to be either argue for separation based upon cultural and religious criterion. But taken as a whole, Italian Fascism's various Jewish policies were antisemitic and had the elimination of Jews from Italian society as its ultimate goal.

Although some of his later defenders would gloss over this, Mussolini's writings in Avanti and Il Popolo d'Italia both before and during the First World War occasionally dabbled in antisemitic vitriol. Mussolini did attack the Jews as the cause of the fall of the Roman Empire and alluded to the Jewish control over various industrial and governmental interests. However, antisemitism was never really a central plank of the emerging ideological goulash that was Fascist thought. As such, Mussolini's antisemitism was reflective of a tactical political maneuver to slur enemies of the movement. The NSDAP's antisemitism was much more central to its political and ideological platform. Mussolini would selectively instrumentalize antisemitism in his seizure of power, sometimes attacking prominent Jews like the Foreign Minister Sidney Sonnino in the Fascist press, while simultaneously declaring during the March On Rome that, "Italy has never known antisemitism and, we believe, will never know it."

But once in power, Mussolini's Jewish policy tread a very fine line between an exclusionary racism and maintenance of a stabilizing status quo. Prominent Jewish supporters of the Fascist Party like Oscar Sinigaglia found themselves ostracized from the corridors of power. The state-controlled press organs also found in both Zionism and "Jewish finance" convenient symbols of foreign interference to the New Order. Yet actual Fascist policy towards Italian Jews in the 1920s to the mid 1930s was relatively ambiguous with official discourse occasionally treating the Jews as an alien entity, but with little in the way of concrete state policies to back these exclusionary ideas with state power. This balancing act became much more difficult after 1933 with the rise of Hitler when Mussolini sought to both distinguish his regime from this new great rival, but also tailor the state to fit into the German model of racialized classification that appeared to be in ascendancy in interwar Europe. The enactment of racial laws in 1938 adapted elements of the Nuremberg Laws for the Italian population. Unlike prior Fascist laws that impacted Jews, the 1938 laws targeted Jews as a total group and referred to Jews as members of a separate race from Italians. Like their German precedents, these new laws defined "Jewish" based on ancestry rather than current religious affiliation. The laws also enacted a sweeping elimination of Jews from Italian state institutions, the Fascist Party, and education. Only a few Jews, the Discriminazione, who had demonstrated value to the Fascist state, served with distinction during the First World War, or were supporters of the Fascist Party prior to the March on Rome, were exempt from these laws. But, as with all protected statuses, this privilege was highly conditional and subject to the state's prerogatives. Yet, unlike the Nuremberg Laws, the 1938 racial laws did not eliminate Italian citizenship for Jews. So unlike German Jews, who were rendered as stateless individuals by the Third Reich's antisemitic policies, Italian Jews were still Italian subjects, albeit with an extremely restricted social role in the Fascist state.

This legal and social limbo remained one of the dominant leitmotifs for Italian Jewish life between 1938-1943. Jews found themselves forced into lower-paying jobs and subject to increased harassment. Italian belligerence in 1940 led to increased restriction on Italian Jews' daily lives and a new round of antisemitic legislation. The state enacted policies of forced labor for Jews, confiscated their radios, and treated the population like a foreign entity.

Despite these new restrictions, Mussolini resisted German calls for further restrictions on Jews. However, such foot-dragging on Mussolini's part was of a piece with Germany's other allies such as Romania or Hungary. These Axis governments too had enacted various antisemitic legislation, both at German prompting and of their own volition, but balked at German calls for more radical measures. This resistance had little to do with Judeophillia and more to do with protecting the remnants of national sovereignty in the face of a German-dominated political imperium. Tellingly, the more dependent (or vulnerable) these states were on German power, the more their protection of their Jewish population fell by the wayside.

Although Italian Fascist antisemitism never reached the levels of National Socialism's violent hatred, which is a very low bar, the logical end of its Jewish policies was the exclusion and social death of Italian Jewry. The Fascist conceptualization of the New Man left little room for Jewishness. Although Italian Jews were fairly well integrated into Italian society prior to the March on Rome, they were ensconced in the older Italian Liberal structures that Fascism portrayed as part of a decayed old order. Although biologically-based antisemitism did not find many partisans among Fascist intellectuals, its few paladins like the pro-German Fascist Roberto Farinacci were far from outliers inside the Fascist intellectual milieu. Prior to 1938, Fascist writers often conflated antisemetic tropes with other stock archetypes such as anti-intellectualism and anti-Marxism. Even in the absence of official doctrinal antisemitism prior to 1938, the Fascist state provided few disincentives against its supporters from engaging in antisemitism. German pressure helped enable the exclusionary tendencies that were present in the Italian Fascist project since the beginning.

Sources

Bosworth, R. J. B. Mussolini's Italy: Life Under the Dictatorship, 1915-1945. New York: Penguin Books, 2006.

Gregor AJ. Mussolini's Intellectuals: fascist social and political thought. Princeton, NJ: Princeton University Press; 2005.

Zimmerman, Joshua D. Jews in Italy Under Fascist and Nazi Rule, 1922-1945. Cambridge: Cambridge University Press, 2005.