Police released few details about the case Wednesday night during a brief news conference and declined to elaborate, other than to say it involved someone who Varlamov was in an intimate relationship with.
Sgt. Steve Warneke said the 25-year-old Russian goalie went to police Wednesday at about 6 p.m. Warneke didn't know if Varlamov had an attorney.
An email was left by The Associated Press with Varlamov's agent.
The Avalanche said in a statement they were aware of the allegations but wouldn't comment further until the conclusion of the investigation. Varlamov practiced with the team earlier in the day.
Varlamov was still in custody Wednesday night, and was due in court for his first court appearance at 10 a.m. Thursday, according to the Denver County sheriff's website.
Asked if Varlamov will be treated any differently in custody because of his celebrity status, Warneke said: "I don't know what happens once they get to Denver Sheriff's, if they do any particulars for high profile, in regards to keeping them safe.
"I do know we consider every criminal prosecution equally important," Warneke said. "We're concerned about the rights of the victim, the rights of everybody involved.
Acquired from Washington in a 2011 trade, Varlamov is 7-1 this season with a 1.76 goals-against average. On Sunday night, he made 24 saves in a 3-2 home victory over Winnipeg.
The Avalanche play at Dallas on Friday night and Varlamov was scheduled to start. His backup, Jean-Sebastien Giguere, has been just as good in net, recording two shutouts.
Varlamov is in the midst of a resurgent season under new coach Patrick Roy and a staff that includes goalie guru Francois Allaire, who once mentored Roy and Giguere.
Between Roy and Allaire, they've restored Varlamov's confidence a year after he allowed three goals a game. Varlamov said he credits his improvement to Allaire altering his form in goal. Just minor tweaks, he said, but wouldn't elaborate on the specifics of what they were.
Whatever was changed, it has been paying off as he's among the NHL leaders in goals-against, wins and save percentage (.945).
After practice Wednesday, Avalanche defenseman Erik Johnson said it was "pretty cool to see Varly transition into an elite NHL goalie."
Associated Press Writer Ivan Moreno contributed to this report.