A 19-year-old has already been fined for riotous behaviour following Thursday's post-match dust-up after Richmond's 33-point victory over Carlton.

Victoria's police boss said the matter was being investigated further.

"Initially there were fines, but looking at the footage, it's serious enough to warrant an affray investigation," Chief Commissioner Graham Ashton told SEN radio on Tuesday.

Video of the brawl shows a group of at least six men, one wearing a Tigers guernsey, throwing punches as dozens of shocked patrons watch.

Mr Ashton said while violent incidents at footy matches hadn't increased, the severity of the violence had.

"On Friday night, for example, we had a couple of fights at the MCG that we're dealing with and a police member was assaulted outside the ground," he said.

"The level of violence is getting worse - but that's not just a footy issue, it's a whole-of-society issue."

Last week, AFL boss Gillon McLachlan labelled the brawl "incredibly disappointing" and "completely unacceptable", while flagging the league's intention to take action.

No bans have been imposed on those involved in the fracas, the AFL confirmed on Monday.

Australian Associated Press