Varlamov, 25, was arrested after a complaint, apparently filed by his girlfriend, alleged that on Monday he kicked the woman, knocked her down and dragged her by the hair, Denver police said.
Varlamov surrendered to authorities about 6 p.m. Wednesday.
He was taken before a judge Thursday where bail was set at $5,000 and Varlamov was given permission to travel. The judge also issued a restraining order, The Denver Post said.
The Post quoted the alleged victim's attorney as saying the woman had been beaten several times. The alleged victim's name was redacted from official court documents released to the public.
The Colorado Avalanche issued a statement about the arrest, saying only that the team was aware of the incident and wouldn't comment. The NHL put out a similar statement.
Varlamov is in his sixth season in the NHL. He played for the Washington Capitals prior to joining the Avalanche before the 2011-12 season. He's played in eight of Colorado's 11 games this season, winning seven and allowing 14 goals.
The Avalanche have 20 points this season, second-most in the NHL. Colorado next plays Friday at Dallas. It was unclear whether Varlamov would make the trip.
Megyn Kelly: Santa Claus and Jesus are both white men
Penelope Cruz named 2013's 'Best Body' by Fitness magazine