It follows an incident “in or around the 50th minute” of the 1-1 draw, when referee Michael Oliver gave the Reds a penalty, penalising Gael Clichy for a raised boot on Roberto Firmino.
James Milner scored from the spot.
City have until 18:00 GMT on Thursday, 23 March to respond to the charge.
Milner’s goal gave Liverpool the lead but Sergio Aguero ensured City took a point from a thrilling draw at Etihad Stadium.
Both Clichy and David Silva were booked after Oliver pointed to the spot.