The midfielder was shown a second yellow card in the 86th minute at Old Trafford for pulling back Memphis Depay just outside the area.
Drinkwater reacted angrily towards referee Michael Oliver but the incident was not reported by the official so will not be taken any further.
The 26-year-old therefore avoids the fate of team-mate Jamie Vardy, who saw his ban extended to two matches after venting his fury at his sending-off against West Ham last month.
Drinkwater will still serve a one-match ban for the red card, ruling him out of Saturday's clash with Everton, which could see Leicester clinch the Premier League title.
Manager Claudio Ranieri said: "I am very sad because he will miss the next game at home."
Leicester and Manchester United will have to wait until Tuesday to find out whether either Robert Huth or Marouane Fellaini will be charged for their off-the-ball altercation.
Fellaini was picked up by TV cameras swinging an elbow at Huth after the Leicester defender had pulled his hair.
The Football Association will wait for Oliver's report before deciding whether further punishment is warranted for either man.
