WFAA-TV in Dallas reported that McCann was taken to a Dallas detox center early Saturday morning at 3 a.m. CT and released almost eight hours later.
In a statement released Sunday morning, McCann denied he was drunk.
"I was not intoxicated and did not pose a danger to myself or others," McCann said in a statement released through his agent, John Biggins. "I am very grateful that, due to the Constitution and Americans' strong and enduring belief in due process, I am presumed innocent of this public intoxication charge because I am innocent."
Cowboys officials were not available for comment.
All NFL players are subject to the personal conduct policy even though the league has locked out the players.
If it's determined McCann violated the conduct policy he will be punished once the lockout is over and his case is reviewed by league officials.
As a rookie, McCann returned an interception 101 yards for a touchdown in a victory against the New York Giants. McCann, an undrafted free agent who went to SMU, also was a kick returner for the Cowboys.
"My good name and reputation mean everything to me," McCann said in his statement. "I have never been arrested before and take pride in conducting myself at all times in a responsible and respectful manner off the football field."
Calvin Watkins covers the Cowboys for ESPNDallas.com.