The alleged offense occurred Oct. 7, but the charges were not filed until Wednesday in the 15th District Court in Ann Arbor, Michigan. The charge is punishable by imprisonment for not more than five years or by a fine not more than $2,500.
Smith, a senior, is being represented by attorney John Shea.
The alleged offense occurred the day before Michigan played against Indiana, a game in which Smith participated and recorded five total tackles.
Smith will continue to participate with the team, athletic director Warde Manuel said Thursday.
"We are aware of the charge against Mazi from a traffic stop back in October," Manuel said in a statement. "Mazi was honest, forthcoming and cooperative from the very beginning and is a tremendous young man. He is not and never has been considered a threat to the university or community.
"Based on the information communicated to us, we will continue to allow the judicial process to play out. Mazi will continue to participate as a member of the team."
Smith has played in all 12 games this season for the No. 2 Wolverines and has accumulated 43 total tackles in Michigan's undefeated season. The team is set to play against Purdue in the Big Ten championship and has a very good chance of making it to the College Football Playoff.
"I have respect for our judicial process and with that respect brings confidence that a fair and just resolution is forthcoming," Michigan coach Jim Harbaugh said in a statement. "Mazi's character and the trust that he has earned over the past four years will continue to be considered throughout the process."
Washtenaw County prosecutor Eli Savit said Smith wasn't swiftly charged in October because he wasn't immediately arrested, which allowed for further investigation of the incident.
"When a defendant is not in custody, authorization of charges generally moves slower. It was a wholly unremarkable timeline when a suspect isn't in custody,'' Savit told the Detroit Free Press.
Smith is also ranked as a top-five defensive tackle in the upcoming NFL draft by ESPN NFL draft insiders Mel Kiper Jr. and Todd McShay.
The Associated Press contributed to this report.