McNary, primarily a special-teams player for the Colts, was charged Wednesday with rape, criminal confinement with bodily injury and battery resulting in bodily injury from an incident in the early-morning hours of Dec. 1, 2014. A not-guilty plea was entered on behalf of McNary on Thursday.
"After reviewing the documents supporting the very serious criminal charges filed yesterday afternoon against Josh McNary, the Colts have requested Commissioner Goodell to immediately place Josh on the league's Commissioner Exemption list," the Colts said in a statement released Thursday.
"That designation will permit the investigation provided by the league's Personal Conduct Policy to run its course and will afford Josh the opportunity to focus on his defense against the charges. The Colts sincerely hope this extraordinarily serious matter will be resolved expeditiously and that justice will prevail."
McNary will not be allowed to practice or attend games with the team. In corresponding moves, the Colts added receiver Griff Whalen to the active roster and signed defensive end Gannon Conway to the practice squad.
Indianapolis plays the New England Patriots in the AFC Championship Game on Sunday.
McNary's attorney released a statement early Thursday morning that said his client "unhesitatingly" is denying the allegations. McNary reported to the police Wednesday night.
In the police report released Wednesday, the woman, whose name was redacted, said she told McNary, 26, to stop.
The police wrote in the statement that when they arrived at McNary's apartment to investigate, McNary said: "I know why you're here." The report said McNary claimed to have preserved evidence because he expected the police would be coming.
The woman claimed she and McNary engaged in a "physical fight" and that she scratched his neck, face, back and shoulder before the alleged sexual assault took place. According to the report, the woman also said she believed the man slapped her on the left side of her face with his hands before forcing himself on her.
A nurse found dried blood behind the woman's ear and other injuries after a sexual assault examination and that a friend of the accuser played a two-minute voice mail from the woman for police, according to the report.
McNary has spent the past two seasons with the Colts. He played at Army and then served two years on active military before signing with the Colts in 2013. McNary still serves in the National Guard as part of his military obligations.
The Associated Press contributed to this report.