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.
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.
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(Reporting by Martyn Herman, editing by Pritha Sarkar)
