The Daily Record reports that Scottish football’s governing body is reviewing the melee which occurred at the end of the match, won 2-1 by Celtic thanks to a late winner from James Forrest.
Rangers left-back Andy Halliday confronted Brown after the Celtic skipper celebrated in front of the away fans.
If Brown is deemed to have committed actions that could have incited the crowd he will be hauled into Hampden Park for a disciplinary meeting.
Halliday received a second yellow card for his part in the scuffle and will be suspended for Wednesday’s match with Hearts. Rangers sub goalkeeper Wes Foderingham and Celtic defender Mikael Lustig were also cautioned.