Internment of some type was a rather standard practice and practiced by pretty much every allied nation. Canada had a rather similar program to the US where they were they removed every male of Japanese origin between the ages of 15-50(not quite sure of the upper limit basic military age) from the pacific coast area.

The English practiced internment as well on people of German and Italian decent that were living in England at the time, the Isle of Mann was used for most of the camps.

Although as u/Gustav55 points out, internment of some sort was indeed common to combatant nations, I think he skims the rather massive implications this had for a nation that, both internally and internationally, proclaimed that it was entering this fight to illustrate the triumph of democracy on the world stage.

Certainly, the Japanese used this American unconstitutional practice to their advantage when appealing to Japanese-Americans for allegiance, loyalty, and help. For that matter, the correct term in the historiography is actually "incarceration," rather than interment. As the Japanese propaganda of the time did rightly note, the US was imprisoning its own citizens in vastly higher numbers than actual non-citizen Japanese immigrants; internment is a term that only applies to the containment of alien subjects, while incarceration accurately describes the abrogation of the rights of citizenship that most Japanese-Americans could rightfully lay claim to. With such oppression under the American government, Japanese Americans were encouraged to conflate their RACE with their rightful loyalties in the war, rather than their CULTURE, which for many, was American, or Japanese-American. Without justifying incarceration, rather because of incarceration to a certain degree, this Japanese propaganda did have some success, as illustrated by the intense internal divisions within the incarcerated communities; nisei (second-generation immigrants born in the US) were more likely to stay loyal to the US, and in turn were allowed to be recruited for the draft and serve in the army to escape incarceration (they were not sent to the Pacific front, but to the European front, though). This made for HUGE internal divides, and accusations of betrayal on all sides within Japanese-American communities.

It was not only the Japanese Empire and Japanese Americans who descried the unconstitutionality, lack of democracy, and indeed, hypocrisy, that came with incarceration, however. Regular red-blooded Americans did mobilize, in however small numbers, to see their neighbors disappear and their communities impoverished and disrupted. Part of this was because of one of the more nefarious motivations for incarceration; Japanese Americans had worked hard and long, some arriving long ago in California, to acquire and work what now amounted to large percentages of the most fertile land in California's valleys. This land was seized and incorporated into larger farming conglomerates controlled by already-rich Anglo-American grower-planters, so now huge growing operations stood where a patchwork of family operated vegetable patches had previously.

The best source on this (my favorite of the many written) is Brian Masaru Hayashi, Democratizing the Enemy: The Japanese American Internment (Princeton, N.J.: Princeton University Press, 2004).

As far as other nation's reactions to the internment, the critiques did not come largely from our Allies; think of how little the US criticized Russia when it was our ally, or Italy (or any of the inhuman regimes we currently support around the world for our own gain and profit). As might be expected, the criticisms came largely from the enemy side of things. In the aftermath of World War II, the USSR was particularly keen to point out America's heinous track record with race to decry all our highfalutin talk of democracy, equality, and prosperity as bunk. A great book for looking at this is Penny M Von Eschen, Satchmo Blows up the World: Jazz Ambassadors Play the Cold War (Cambridge, Mass.: Harvard University Press, 2004). Von Eschen tells the story of how, starting in the 1930s, the US State Department sent out African Americans to play jazz around the world to show off American cultural achievements and bely these attacks from enemy powers arguing that US democracy was a cruel farce. The cruelest travesty of all was that Louis Armstrong and other black performers on these tours received better, non-segregated accommodations, more enthusiastic audiences, and higher acclaim abroad than they ever experienced at home, where African American jazz was considered low-brow, cacophonous noise. And race riots and lynchings were happening all over the place at home. So yeah, the USSR and other enemy powers had a lot of easy pickings to criticize us for, including the Japanese internment (ironic because the Russians had such respect for their Japanese allies prior to that, no?).

In conclusion, yeah it totally hurt the US's credibility as an altruistic, idealistic, democratic nation, both internally, and on the world stage, although as the biggest kid on the playground, no one was going to point it out except those already with a bone to pick.