Gattuso handed four-match ban
"The control and disciplinary body ruled that Gattuso had assaulted the Tottenham Hotspur assistant coach Joe Jordan after the match," said UEFA.
Gattuso would have missed the second leg of the round-of-16 tie in any case after being booked during the first leg, which Tottenham won 1-0, and accumulating a third yellow card.
"Consequently, the four-match suspension applies to the next four UEFA club competition matches for which he would be eligible," UEFA said.
The new ban means Gattuso, 33, will miss the quarter-finals and semi-finals should Milan progress that far and could only play again in the final.
Gattuso, who has apologised for the incident, grabbed Jordan by the throat and pushed him on the touchline during the game, and headbutted him after the final whistle before being pulled away by team mates.
He has the right to appeal within three days.
Jordan, with his trademark missing teeth, won a reputation as a hard man during his days as a striker with Leeds United, Manchester United, Milan and Scotland.