The 24-year-old Colombian internationalist faces a three-game ban if the Ibrox side choose to appeal the notice of complaint.
Should Rangers fight the charge, a hearing will be held on Tuesday February 2.
Morelos stamped on the Easter Road defender during the first half of the Scottish Premiership clash on Wednesday night, with match referee Kevin Clancy telling players the flashpoint was merely a “tangle of legs" after taking no action at the time.
Hibs defender Darren McGregor has escaped a similar charge for an incident with Gers midfielder Glen Kamara. With no compliance officer currently in post, three former referees study incidents before making a decision on further action.
It is understood that the panel did not believe McGregor's challenge on Kamara constituted violent conduct, with the veteran defender booked for reckless play at the time.