Following the 5-2 loss the Croat said he wanted an explanation for why Dominic Calvert-Lewin’s first goal for Everton was awarded by the video assistant referee, having initially been ruled out.
An FA statement said: “It is alleged that the West Bromwich Albion FC manager’s language and/or behaviour on the field of play at half-time of the Premier League fixture against Everton FC on 19 September amounts to improper conduct.”
The charge could result in up to a two-match touchline ban if evidence of abusive or insulting language is found.
“The analysis guys told me it was a foul for us before their first goal,” Bilic told BBC Sport on Saturday.
The 52-year-old added: “As a manager I should be in a situation to ask the referee what’s going on.
“It’s not like the game was going on, it was half-time – nobody was around. I didn’t swear. I asked him in a frustrated way but I didn’t go over the line. But he just ignored me and gave me red.
“As a manager you have that right if you are not crossing the line. I told him if you want to kill us, kill us. That’s all.”
West Brom lost their first two games of the Premier League season, conceding eight goals in the process.
Defender Kieran Gibbs was also sent off just before half-time on Saturday for a push on James Rodriguez.