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