The England international will be suspended following an elbow on Watford's Valon Behrami in the Foxes' 2-1 defeat at Vicarage Road on Saturday.
Referee Neil Swarbrick took no action during the game but the FA acted having been alerted to the footage after it ran on social media on Sunday.
Drinkwater will now miss Saturday's visit of Middlesbrough, the trip to Sunderland and the home game with Manchester City on December 10.
He has started every Leicester game this season and helped them into the last 16 of the Champions League on Tuesday when the Foxes beat Club Brugge 2-1.
His ban leaves boss Claudio Ranieri light in midfield, with Nampalys Mendy struggling with an ankle injury, while Matty James has not played for 18 months following a knee injury. Andy King and Daniel Amartey are the club's only fit senior central midfielders.
Defenders Robert Huth and Danny Simpson are also just a booking away from a one-match ban.Reuse content