The 19-year-old, on loan from Championship side Bolton, has already served an automatic two-game ban for the incident which resulted in a red card during the match against Dunfermline.
Fraser had been accused by the SFA compliance officer of punching Dunfermline's Chris Kane and kicking him repeatedly on the head and body.
A Thistle spokesman said: "Gary, who is on loan at Firhill until 4 January, has been given an additional seven-game ban. He will be available again for selection from 1 January onwards."
Speaking last month, manager Alan Archibald said: "He just said the red mist came down and he retaliated. He knows he let himself down.
"I am hoping we can keep him until the end of the season but it is too early
Fraser joined Bolton from Hamilton in the summer before moving to Firhill on a six-month loan agreement.
He played in newly-promoted Thistles' first four Scottish Premiership games but has not featured since August.