"It is alleged they failed to ensure their players conducted themselves in an orderly fashion during the fifth minute of the fixture," the FA said in a statement.
Both clubs, which play in the second-tier Championship, have until March 18 to respond.
A Birmingham City fan was jailed for 14 weeks on Monday for running onto the field of play and punching Grealish later on in the match.
Grealish went on to score in the second half to give Villa a 1-0 victory.
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(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by David Goodman)
