The incident, which occurred during the second half of the Premier League champions' 2-1 defeat at Vicarage Road on Saturday, was not spotted by match officials at the time but was caught on camera.
Drinkwater has been given until 6pm GMT on Wednesday to respond to the charge, which has been referred to a panel of former referees.
An FA statement read: "Off the ball incidents which are not seen at the time by the match officials are referred to a panel of three former elite referees.
"Each referee panel member will review the video footage independently of one another to determine whether they consider it a sending-off offence.
"For retrospective action to be taken, and an FA charge to follow, the decision of the panel must be unanimous."