The 38-year-old, who joined Steve Cooper’s coaching staff 12 months ago, may face a fine or touchline ban.
Former Swans player Tate looked to have grabbed the Blues’ Spanish midfielder Toral’s throat as players left the field at half-time.
The incident sparked a melee involving players and staff from both sides followed, but no action was taken at the time.
“A Swansea City FC coach, Alan Tate, has been charged with a breach of FA Rule E3,” an FA statement said.
“It is alleged that his behaviour at half-time of the EFL Championship fixture against Birmingham City FC on Saturday [19/09/20] amounts to improper and/or violent conduct. He has until Friday [25/09/20] to respond to the charge.
Swans boss Steve Cooper and opposite number Aitor Karanka both said they did not see what happened.
Cooper said after the 0-0 draw: “I didn’t see it, clearly. It certainly didn’t carry on down the tunnel because I went down there. Afterwards, it was fine – no dramas.