He barged the official with his chest in the fourth minute of stoppage time at the end of last Saturday's game.
Bacuna, 25, admitted a charge of violent conduct "in circumstances where the standard three-match ban would be clearly insufficient".
The Curacao international has made 25 appearances for Villa this season.
Born in the Netherlands, he joined the club from Groningen for an undisclosed fee in the summer of 2013.
His dismissal was the first time he had been sent off while playing for Villa.
Speaking after the game, boss Steve Bruce told BBC WM Sport 95.6: "Bacuna's overstepped the line with his antics in the last minute, but I thought he was terrific.
"He was everything I would ask for, then he lets himself down."
Bacuna has already served one match of his ban, having sat out Tuesday's 2-0 victory over Bristol City.
Aston Villa midfielder Leandro Bacuna has been banned for six games following an altercation with an assistant referee in their home win over Derby.