Drinkwater appeared to elbow Watford's Valon Behrami during his side's 2-1 Premier League defeat on Saturday.
It was missed at the time by the match officials but after watching video evidence the FA charged the 26-year-old.
The automatic three-match ban starts with immediate effect meaning Drinkwater will miss the matches against Middlesbrough, Sunderland and Manchester City.
Manager Claudio Ranieri said Drinkwater was 'sorry' for his actions.
“I think he made a mistake. I think it is right to accept the charge. He is so sorry, but that is the law and we accept,” Ranieri told reporters on Thursday.
“Of course, he is not happy. He wanted to play, but he is okay. I hope we don't miss him. It is important that the group, together, supports this fate.”
Leicester are 14th in the Premier League, two points above the relegation zone, although they have qualified for the last 16 of the Champions League as group winners following Tuesday's 2-1 victory over Club Bruges.
Original source: Leicester's Drinkwater banned for three matches