The FA confirmed that United, who were knocked out of the competition at Stamford Bridge on Monday night, accepted their charge for failure to control their players after Ander Herrera had been sent off.
The midfielder was shown a second yellow card for two fouls on Eden Hazard within 15 minutes of each other during the first half of the quarter-final tie which triggered off protests by the United team to referee Michael Oliver.
United admitted the charge and have now been fined £20,000.
A statement on the FA's website on Friday read: "Manchester United have been fined £20,000 after the club admitted an FA misconduct charge and accepted the standard penalty.
"It relates to a breach of FA Rule E20(a) for failing to ensure its players conducted themselves in an orderly fashion in or around the 35th minute of their Emirates FA Cup quarter-final against Chelsea on Monday 13 March 2017."