Police ejected 16 fans after a brawl erupted inside the stadium before kick-off and dispersed rival fans from a pub nearby.
FFA has called for police and security reports and will view a video of the incident inside the stadium, which involved up to 30 Sydney and Melbourne fans.
Bonita Mersiadis, FFA head of media communications, said no arrests were made inside the stadium or outside the pub.
"However, we are disappointed with what happened," Mersiadis said.
"The FFA, in conjunction with the police and the security company, have worked hard to ensure there are no problems at any of our matches.
"We have asked for reports and we will consider the next step after we have studied them. Hopefully we will be able to identify the culprits. We certainly have the option of banning the fans from all A-League games in the future, as well as any internationals that come under our jurisdiction.
"It should be pointed out that it is only a very small group of fans who are intent on causing problems while the vast majority of true football followers behave themselves impeccably."
Saturday night's problem is not the first involving the two clubs.