So huge disclaimer before I leap into this: Reliable data for this in English sources is practically non-existent. The actual Soviet censuses themselves are not entirely trustworthy, and most English language sources are either relying (out of necessity) questionable sources or are from openly Marxist organizations. The best we can therefore do, with the plethora of misinformation and bad methodology that plagues this issue, is frame and guess.
The nearest census prior to the outbreak of war in the Soviet Union is the 1939 census. Which unfortunately has gross evidence of number distortion and thus should be taken with a grain of salt. Likewise for the Census of 1937; it is incredibly obvious that the numbers of persons reported were significantly lower than the actual population numbers. The 1937 census was so disastrous that the individuals responsible for it were strongly censured and imprisoned for their incompetency (and accused of active sabotage by a paranoid Stalin).
However, that being said, its the best we got. So let's guesstimate:
The furthermost extent of the Nazi's penetration into the USSR was gained in October 1941 when they began to bog down in front of Moscow. At this point in time, the Axis occupied a line from the southern tip of Lake Lagoda to the Sea of Azov on the Crimean Peninsula. With the notable exemptions of Leningrad (which by this point in 1941, had probably 600, 000 civilians still alive within its confines) and Sebastopol and the Prippet Marshes, all large pockets of resistance in the rear were crushed.
This means that, very roughly (as we cannot count for displaced persons or refugees causing ebb and flow), and without further information: The entirety of the Ukranian SSR, Lithuania , Latvia and significant portions of "White Russia" were under German control. These are largely considered the most populous regions of the Soviet Union, despite the crushing famine and deathtoll that occurred not long before the war in the Ukraine SSR.
The problems arise here: Its very hard to find the population of individual SSRs in English language sources, and even if one does, we are reminded that the 1937 and 1939 censuses are deeply erroneous.
Consider this table; and note the discrepancies between projected and actual population.
The estimated population of the Ukraine SSR is approximately 41 million based on the 1939 census. This is compared to a total population of approximately 200 million for the entirety of the USSR. Reliable data (in a very relative sense of the word) does not truly exist for populations of other SSRs in this time period. We only have the knowledge, therefore, of the approx. 200 million (very much so approximate) in total and the knowledge that significant portions of that population resided West of the Urals and Caucuses, with at least 41 million in the Ukraine SSR alone. We also must take into account the annexed territories immediately prior to the invasion of 1941 which the Germans quickly captured in June and July of 1941; such as Eastern Poland, which probably netted at least 30 million persons.
The population of the Soviet Union on June 22, 1941
209.3 million people.
Far from all inhabitants of occupied by Germany regions the Soviet Union were able to move to the rear. For various reasons behind the front left about 70 million Soviet citizens.