It depends on your definition of "concentration camps". Stalin certainly set up labour camps all throughout his time in power, not just during WWII. People were sent there for basically not agreeing with Stalin's agenda. The system of camps (many of them in Siberia) and prisons is known as Gulag. I recommend the book The Gulag Archipelago by Aleksandr Solzhenitsyn which offers insights into the Gulag as Solzhenitsyn himself spent some time there.

As for the number of victims, no one knows for sure. People weren't gassed like in Nazi concentration camps, but rather worked to death. There were many more Gulag camps than concentration camps and the system lasted longer. About 14 million people are said to have been in Gulag camps at one point or another, and the estimates for death tolls ranges between 1 million and 10 million.

First off, if you do not know about the Gulag system, you may want to have a look around for resources about this.

Okay, on to some observations and data. The first thing to note is that concentration camps had been around in Russia for decades by the time the Second World War started - long before Stalin came to power Lenin had created the first (small) concentration camps, which were set up already in 1918 (Jensen, Gulag og Glemsel (Danish source)).

The conditions for people living in the GULAG camps had never been worse than they were during the war. Deaths increased a lot during the war; it's been estimated that when counting executions and other deaths of people in prisons as well as work camps, around 600.000 people perished during the years of 1941-43 alone in the Gulag system. According to the official numbers, there were 1.672.438 people in the Gulag system in the year 1939; the numbers vary by hundreds of thousands over the next years, reaching almost 2 million (1.929.729) in 1941 and then decreasing in the years thereafter, reaching 1.460.677 in 1945, again according to official estimates. The numbers increased after the war, to almost 2.5 million in 1953. There's a huge discussion about which numbers and estimates are best and lots of people don't trust the official numbers, but there's no doubt a lot of people from Eastern Europe spent time in Soviet concentration camps during the war, nor is there any doubt that a lot of them died there. Ethnic minorities such as e.g. Crimean Tartars as well as people living in occupied territories (e.g. the Baltics) were also vulnerable during this period, as large-scale deportations of such groups were undertaken (~42.000 people during two days in June during 1944, ~90.000 in November - this kind of stuff also incidentally happened earlier in the war; roughly 450.000 Germans were deported by the Soviets during September 1941 (Courtois, Werth, Panné et al)), and by the 25th of december that number had grown to 894.600. Often such deportations happened in ways that caused high death rates - people were frequently deported to poorly developed areas, without even being given enough food or clothes to survive, and many died from starvation, hypothermia or disease.

Deaths were caused by various factors including starvation (in 1942 the number of calories allotted to each prisoner had fallen by 65% on average, compared to the pre-war norm), as well as executions and epidemics - typhus and cholera epidemics according to the official numbers caused approximately 19.000 deaths in 1942. In the work camps the mortality rate in 1941 was roughly 8%, with 101.000 deaths. In 1942 the number of deaths had increased to 249.000, corresponding to a mortality rate of 18%, and in 1943 the numbers were 167.000 and 17%. Many people who left the camps during those years went directly from a labor camp to the front line; when including people who had served their time, more than 1 million people (1.068.000) went directly from Gulag to the front line. There was also traffic going the other way; during 1941 from July to December, 750.000 Soviet prisoners (from 210 colonies, 135 prisons, and 27 camps) were relocated to the east because of the German advance. When there wasn't enough time to evacuate the camps, the Soviets would execute the prisoners - this happened for example in Lvov during the end of 1941, where 10.000 people were executed and put into mass graves later found by the Germans.

The Soviet camps varied in terms of how dangerous they were; the average mortality rates are averages and hide quite a bit of variation - some of the Siberian camps in particular had significantly higher mortality rates than the rest. There's some discussion about whether/to which extent parts of the Soviet camp system served similar purposes as did the German extermination camps, although as stefan2494 also notes the methods used to kill people were different (worked to death, vs gas).

As you can tell from the numbers above, most likely fewer people died in Soviet camps during the war than died in German camps. But the Soviet camp system was quite big and did affect millions of people. It also lasted a lot longer than did the German camp system, making comparisons more complicated than they otherwise would be.

Most of the numbers above are from Courtois, Werth, Panné et al's coverage. I'd have quoted from the work, but unfortunately I only own a Danish edition of the book, so this was not possible.