The Italy international was punished by the Italian football league (Lega Serie A) after being shown his second yellow card for "insulting and intimidating the referee" after the final whistle.
It represents a turnaround by the Serie A club who on Monday said they would appeal the decision.
However, the club will launch an appeal against the Lega Serie A's decision to close the Curva Sud for one game - Milan were ordered to close that section of the Giuseppe Meazza stadium for their next home game for racist abuse directed at Napoli fans.
A statement from Milan read: "AC Milan announces it will appeal against the closure of the Curva but it will not appeal against Mario Balotelli's ban."
Balotelli, who is Milan's top scorer with three goals in four league games this season, will miss the Rossoneri's encounters against Bologna, Sampdoria and Juventus.