The New York Times reports that Russian outlets said Fedotov was arrested at a St. Petersburg hockey rink on Friday and taken to an army enlistment office.
There is a mandatory one year of service for Russian men.
The Flyers signed Fedotov to an entry-level deal in May. The 25-year-old helped CSKA Moscow win the KHL title this season, going 14-10-2 with a 2.00 goals-against average and .919 save percentage.
Fedotov also helped the Russians win silver at the 2022 Beijing Olympics.
The Flyers picked Fedotov in the seventh round (188th overall) of the 2015 NHL Draft.
In a statement to the Philadelphia Inquirer, Flyers GM Chuck Fletcher said: “We’re aware of the reports and are investigating the situation. We have no further comment at this time.”