Andy Halliday angrily confronted Scott Brown after the Celtic captain celebrated in front of the away fans in the aftermath of the hosts’ 2-1 victory.
This led to a melee with several players on both sides getting involved in a pushing match.
Halliday was shown a second yellow card for his part in the drama, while Rangers substitute Wes Foderingham and Celtic defender Mikael Lustig were also booked.
Hearts and Hibs were each fined £10,000 over player behaviour in the 0-0 Edinburgh derby draw back in October, and the two Glasgow clubs could receive the same punishment.
Ross County and Inverness CT were also fined £2,500 each for a similar brawl.