A conviction would mean a maximum 60 days in jail and a $500 fine, though defendants often avoid jail time for such offenses. Williams, 21, was arrested Tuesday after a traffic stop.
Two others with him in his SUV at the time face more serious charges.
Roosevelt Rollins, 21, Memphis, Tenn., is charged with possession of marijuana. The Class A misdemeanor carries a maximum penalty of one year in jail and a $5,000 fine.
Another passenger, Roderick Helton, 32, Memphis, Tenn., is charged with carrying a handgun without a license as a Class A misdemeanor.
Williams released the following statement, which is on his team's website:
"I am very disappointed that I put myself in this position and I take full responsibility and want to be held accountable for my actions. I want to apologize to Mel and Herb Simon, the Pacers front office, my teammates, my family, and most importantly, the fans. I am accepting the three-game suspension and will not appeal. Again, I want to apologize to my family and the fans and get back to playing basketball and helping the Pacers succeed."