The charge appears to refer to the heated aftermath of West Brom's Claudio Yacob escaping a second booking after fouling Diego Costa in the 56th minute of the 2-2 draw at Stamford Bridge on Wednesday.
Yacob was substituted soon after.
An FA statement said both clubs had until Wednesday to respond to the charge.
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The game was a fractious affair with firebrand Chelsea striker Costa involved in several spats, including an incident with most of the West Brom team after the final whistle.
However, the Spain international looks set to escape any personal charges.
In September he was retrospectively given a three-game ban for violent conduct after the referee missed his tussle with Arsenal's Laurent Koscielny.
(Writing by Mark Meadows; Editing by Tony Jimenez)
