The fight broke out between two men on the Seaford line about 6.45pm after an initial verbal altercation.
“I’m a f—ing beast and you aren’t, so f— off,” one of the men said in video obtained by 9News Adelaide.
“F— off man, you ain’t s—, if you ain’t trained then f— off.”
Another man became involved and held the passenger in a headlock as a man dressed in orange threw punches.
A woman who witnessed the fight pressed the train’s emergency button for help.
The men later got off the train at Oaklands Railway Station.
Transport Minister Tom Koutsantonis vowed to ban the men for life from public transport if they are caught.
“They’re idiots,” Koutsantonis said.
“We cannot tolerate assaults on public transport, we have zero tolerance for it.
“I’ll ban them for life, absolutely.”
Members of the public have called for more security on trains as roaming patrols don’t start until 7pm.
“I think to the peak time would be better,” one commuter said.
“It’d be good to have them during peak hours like 5pm,” another commuter said.
Parking failure sparks ire
An investigation is under way to identify the men and CCTV of the incident will be reviewed.
“We’ve got their pictures, we possibly even have their credit card details and we are forwarding this all on to police,” Koutsantonis said.