The incident occurred in Fulham's 3-1 FA Cup quarterfinal defeat to Manchester United at Old Trafford just before the recent international break.
The Serbian striker put his hands on Kavanagh after the referee awarded Manchester United a penalty and sent off Willian for a handball on the line.
Mitrovic was supposed to serve a standard three-game ban but an independent regulatory commission deemed the punishment insufficient.
Having already missed Fulham's game against Bournemouth over the weekend, Mitrovic will be unavailable for the next seven fixtures.
The former Newcastle United striker has also been fined £75,000.
"We claimed the standard punishment which would otherwise apply to Aleksandar Mitrovic for the sending-off offence of violent conduct that he committed towards the match referee around the 72nd minute was clearly insufficient. The forward denied this, but it was upheld by the Regulatory Commission, and a three-match ban was imposed," a statement from an independent Regulatory Commission read.
"This is in addition to the three-match ban he had already received for the red card offence. The forward separately admitted that his behaviour and language after being sent off was improper, abusive, insulting and threatening, and the Regulatory Commission imposed an additional two-match ban and £75,000 fine. In total, the Regulatory Commission has suspended Aleksandar Mitrovic for eight matches. One of these has already been served, and therefore the forward will be unavailable for Fulham FC’s next seven matches."
Matches Mitrovic will miss include Liverpool, Manchester City and Aston Villa.
The 28-year-old has scored 11 goals in 28 Premier League games this season.
