United have however been charged for failing to control their players in the incident that saw Ander Herrera sent off in the first-half of the tie at Stamford Bridge.
Herrera was booked in the 20th minute of the match for a challenge on Hazard as United attempted to shut down the Belgium international. He was shown a second yellow 10 minutes from half-time for a trip on the same player, with United players crowding referee Michael Oliver to protest the decision.
A brief statement from the FA read: "Manchester United have been charged for failing to control their players.
"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."
Hazard was also involved in the incident with Rojo. After tripping the tricky Chelsea playmaker out wide, Rojo was pictured by television cameras appearing to land his right foot on Hazard's torso. Just a free-kick was awarded for the original offence, which at the time left the Argentina defender open to a retrospective action.
However, the FA have decided to only charge United for failing to control their players in the earlier incident. Oliver has informed the governing body he saw the incident involving Rojo but decided not to take action.