According to the Post, the kidnapping charge is a Class 4 felony -- taking someone without their consent -- punishable by to two to six years in prison.
Varlamov, 25, has been on fire to start the 2013-14 season, posting a 7-1-0 record with the Avs, along with a 1.76 goals-against-average and a .945 save percentage.
The native of Samara, Russia, will spend the night in jail and will appear before a judge at 10am local time on Thursday morning.
Prison officials told the Post Varlamov is along in a cell due to his celebrity status. He refused an interview with the Post, when one was requested.
Members of the Avalanche declined to comment on the situation, but the team did release a statement shortly after news broke:
"The Colorado Avalanche organization is aware of the allegations concerning Semyon Varlamov. At this time, and until the conclusion of this investigation, the Avalanche organization will have no further comment on this situation."