UEFA's disciplinary body "ruled that Gattuso had assaulted the Tottenham assistant coach Joe Jordan after the match," the European football authority said in a statement.
Gattuso earlier grabbed at Jordan's throat in a separate sideline clash during a heated round-of-16 first-leg match in Milan last Tuesday. Tottenham won 1-0.
UEFA charged Gattuso with "gross unsporting conduct" and its disciplinary panel imposed the four-match ban on top of a one-match suspension for receiving yellow cards which already ruled him out of the March 9 return in London.
Gattuso, who captained Milan, must serve the ban in UEFA's Champions League or Europa League competitions.
He can appeal to UEFA within three days.
Gattuso apologized for his behavior when speaking with reporters after the match.
"I take full responsibility. I was wound up after exchanging words with Jordan," the 33-year-old Italy international said.
Gattuso and Jordan, a former Milan player, seemed ready to resume their second-half dispute as soon as the final whistle blew.
After removing his shirt, Gattuso moved quickly toward to the Tottenham bench where Jordan was seen to take off his spectacles as if anticipating a confrontation.
The two men stared each other down before Gattuso nodded his forehead into Jordan's face. They were separated by players and coaches and Gattuso had to be restrained by teammates, but was not shown a second yellow card by French referee Stephane Lannoy.
Now aged 59, Jordan had a reputation as a tough center forward for Leeds, Manchester United and Milan. He played for Leeds in its 1975 European Cup final loss to Bayern Munich and scored for Scotland at three straight World Cups from 1974-82.