The 26-year-old McNary, of Houston, Texas, stands accused of one count of rape, one count of criminal confinement and one count of battery resulting in bodily injury, court documents show.
The alleged incident took place December 1 when the woman visited a few different bars with some friends before she ended up at an “unknown apartment” in the early morning hours with a man she had just met.
According to court documents, the two ended up in the bedroom where he tried to kiss her but the woman said the man got upset when she told him to stop and prevented her from leaving.
“He scared me, intimidated me and scared me,” she told police.
The woman said she grabbed a cellphone as she left the apartment and police say they later traced it McNary.
The Colts said they are still trying to gather more information about what happened.
“We are aware that there has been a report about Josh McNary, but unfortunately that’s the limit of our knowledge,” the team said.
“At this time we are very concerned and trying to find out what the relevant facts are, but we have insufficient information to venture any opinion. As we learn more we will make appropriate updates.”
The NFL recently stepped up its policy for addressing assault and domestic violence following criticism of the way it handled allegations of crimes against women.
McNary, who plays mainly on special teams, appeared in 15 games for the Colts this season, recording 28 tackles.
Indianapolis play the New England Patriots in the AFC championship game on Sunday with the winner advancing to the Super Bowl.