McAfee, who missed practice Wednesday, wasn't available for comment after a short Thursday morning session.
Police say McAfee was found early Wednesday morning with a blood-alcohol content of 0.15 percent, nearly twice the legal limit for driving in Indiana. Police said McAfee swam in a city canal in the city's Broad Ripple neighborhood.
The team said McAfee will miss the Nov. 1 game against the Houston Texans. The NFL also might levy punishment.
"He's been suspended for the Houston game. And then he'll be back after that," Colts president Bill Polian said Thursday, according to WISH-TV. "He made a mistake, he has to pay the penalty for that. And after that, it's business as usual. He's a really good young guy. He just made a mistake and he recognizes it, and we'll move on."
The Associated Press contributed to this report.