The video, filmed by a commuter on the bus, shows a woman yelling obscenities at a mother and child of Asian appearance, and two other passengers who came to their defence.

The rant appeared to be prompted by the fact that the child had not paid for a ticket.

"They're not f---ing people, they're not f---ing Australian, and she didn't pay for her f---ing ticket," the woman was shown shouting.

"Literally they're f---ing invading our country, can't you see it f---ing Chinese people f---ing everywhere."

The two passengers who came to their defence are heard telling the woman, "You're a disgrace", and "That's enough".

The couple, Jenny and Clive Starr, told Channel 9 they comforted the victims afterwards and confirmed they were okay.

SA Premier Jay Weatherill has criticised the racist remarks, saying: "This is not us, this is not who we are."

SA police have declared the incident "not acceptable" and confirmed they will investigate the incident, asking any witnesses to contact police.

The woman could face charges of disorderly behaviour.

Police encourage anyone who witnesses or is the victim of similar behaviour to contact police.