The English Football Association said the Uruguayan had until Monday to respond to the charge.
“Hull manager Steve Bruce has been contacted by The FA in relation to the same incident and formally reminded of his responsibilities,” the FA added.
Poyet was sent to the stands after a heated touchline exchange with Bruce in the 35th minute of the match at the KC Stadium.
“It was grown men acting like children. Look, we all do stupid things but we will all wake up in the morning and regret it,” Bruce said afterwards.
“I am not sure what I am supposed to have done - I only went to his assistant and said that (Jack) Rodwell had dived.”
The game, between two sides fighting to put distance between themselves and the relegation zone, finished 1-1 after Rodwell scored a late equaliser for the visitors.
Poyet said afterwards that Tuesday had been the most difficult day of his managerial career, with Sunderland's England winger Adam Johnson arrested on Monday on suspicion of having sex with an under-age girl.
Sunderland have suspended Johnson while police investigations are ongoing. – Reuters
Original source: Sunderland’s Poyet charged by FA