The flashpoint in question came after of an off-the-ball trip by West Brom's Claudio Yacob, who had already been booked, on Chelsea striker Diego Costa.
The Baggies midfielder avoided a second yellow card and a dismissal before being promptly substituted by boss Tony Pulis in the 2-2 draw.
"Chelsea and West Bromwich Albion have both been charged for failing to ensure their players conducted themselves in an orderly fashion," a FA statement read.
"The charge relates to an incident which occurred in or around the 58th minute of their fixture on Wednesday, January 13, 2016.
"Both clubs have until 6pm on 20 January 2016 to respond to the charge."
Chelsea interim boss Guus Hiddink referred to the incident on Friday.
Hiddink felt Yacob should have been dismissed and was so frustrated with the performance of referee Anthony Taylor that he expressed his concerns to fourth official Jon Moss
He was taken aback by the reply.
"I told him: 'This is one of the worst referees of the Premier League I have experienced,'" said Hiddink, who had a prior caretaker spell at Chelsea in 2009.
"He said to me 'you haven't seen me yet', which was a beautiful remark I think."
Source : PA