Jose Mourinho's men lost 1-0 at Stamford Bridge, with N'Golo Kante's long-range strike proving decisive following Ander Herrera's sending off for two bookable offences.
United's players appeared to crowd referee Michael Oliver as he dismissed Herrera, the Spaniard picking up his second yellow after fouling Eden Hazard.
"Manchester United have been charged for failing to control their players," reads an FA statement.
"It follows an incident in the 35th minute of the Emirates FA Cup quarter final tie against Chelsea at Stamford Bridge yesterday [Monday 13 March 2017].
"The club have until 6pm on Friday 17 March 2017 to respond to the charge."
Marcos Rojo, meanwhile, has not been punished for an alleged stamp on Hazard.
Replays of the incident showed that Rojo brought his foot down into Hazard's chest but the incident was witnessed by referee Oliver, and no retrospective action can subsequently be taken.