Referee Michael Oliver was surrounded by several United players after sending off midfielder Ander Herrera 10 minutes before half-time.
United lost the stormy tie at Stamford Bridge 1-0.
An FA statement said United have until 18:00 GMT on Friday to respond.
Spanish midfielder Herrera was sent off after a second foul on Chelsea forward Eden Hazard.
No further action will be taken against United's Marcos Rojo for an incident late in game.
Rojo appeared to stamp on Hazard but Oliver has told the FA he saw it and dealt with the incident as he saw fit at the time.
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Manchester United have been charged by the Football Association with failing to control their players during Monday's FA Cup quarter-final defeat at Chelsea.