A fan who made a Hitler salute at an Australian football match was banned for life on Wednesday, with the sport's governing body saying it had a zero-tolerance to "offensive behaviour".

The man, who has not been named publicly, was among a group of supporters at the Australia Cup final in Sydney on Saturday caught on camera making fascist gestures and reportedly chanting far-right Croatian songs.

Football Australia said one spectator has been identified and handed a lifetime ban from any future games it sanctions, including national team, A-League and Australia Cup fixtures.

"The conduct in question relates to a fascist salute or similar gesture conducted during the match and captured on the host broadcast," said the governing body, which previously referred to "Hitler salutes".

"Football Australia adopts a zero-tolerance policy to disrespectful and offensive behaviour at sanctioned events and will not tolerate behaviour that has the potential to offend, insult humiliate, disparage or vilify spectators, players or officials."

It added that investigations were continuing to identify other individuals.

Eight people were ejected from Sydney's CommBank Stadium during the match between A-League side Macarthur FC and semi-professional Sydney United 58, formerly known as Sydney Croatia.

The heavy penalty came as Football Australia chief executive James Johnson wrote an open letter to the football community, saying that he was "shocked and concerned" by the fans' behaviour.

"Their actions have disrespected, hurt, and offended members of our football community," he said.

Spectators were also accused of shouting over an Indigenous welcoming ceremony, acknowledging Indigenous people's link to the land.