"It is alleged that his behaviour in or around the 90th minute of the fixture amounted to improper conduct," the FA said in a statement.
The Croatian was sent off by referee Michael Oliver after venting his anger on a pitch-side television microphone following West Brom's injury-time equaliser at the London Stadium.
Assistant manager Nikola Jurcevic was also charged with alleged misconduct after a 19th minute incident that saw him sent to the stands for leaving the technical area to protest an offside call.
Both face possible touchline bans and fines if found guilty of the charges.
"To be fair I am already big time punished with what happened in the game," Bilic had said after the game.
"I don't think that I crossed the line, it was nothing personal. It was the fourth or fifth decision which went against us and it's hard to get over that without reacting."
(Reporting by Alan Baldwin, editing by Pritha Sarkar)
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