The Brazilian-born Spain striker faces a potential three-game ban after he appeared to tread down on the 21-year-old German early in the first half of their League Cup semi-final, second leg at Stamford Bridge on Tuesday.
He was later involved in a second stamping furore involving Liverpool's Slovakian defender Martin Skrtel, but the FA said they would not take any action over that incident.
The FA said in a statement on their website that referee Michael Oliver had not seen the incident involving Can and Costa had been charged after a review of video evidence.
Costa has until Thursday to respond to the charge, but his chances of facing City are in doubt as the FA are prepared to hear any appeal on Friday, according to media reports.
Chelsea reached the League Cup final thanks to a towering header from Branislav Ivanovic in extra time to give them a 1-0 victory on the night and 2-1 aggregate success.
The match took a toll on manager Jose Mourinho's side, however, with midfielder Cesc Fabregas and defender Felipe Luis suffering injuries that could rule them out of Saturday's game.
Chelsea are five points clear of City at the top of the table.
(Reporting by Toby Davis; Editing by Ken Ferris)
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