At least 19 people have been injured, including a toddler, after police say a car intentionally ploughed into pedestrians in the heart of Melbourne, Australia during the pre-Christmas shopping rush.

The terrifying incident saw the white Suzuki SUV collide with pedestrians at the corner of Elizabeth Street and Flinders Street at around 4.40pm local time on Thursday (21 December).

Victoria Police say they believe the act was intentional but that there's no evidence it was terror related.

The alleged driver of the car is a 32-year-old man of Afghan descent who was arrested at the scene by an off-duty police officer.

He has a history of drug use and mental health issues who was known to state police on "historical assault matters", officers said.

Footage from the scene, which would have been packed with Christmas shoppers at the time of the incident, shows him being pulled away from the vehicle by officers.

A second person arrested at the scene, a 24-year-old man, had been filming the incident and allegedly had knives in his bag. Detectives no longer believe he is involved, however.

Among the 19 people injured, four are in a critical condition. A pre-school aged child who suffered head injuries is in a stable condition.

One witness, James Unkles, told local radio station 3AW the car had "just mowed everybody down, people were flying everywhere".

He added: "I immediately had to turn back because police were everywhere trying to get control of the scene. It was chaos everywhere you looked."

Another witness, Lachlan Read, told the Herald Sun the whole incident lasted about 15 seconds.

Describing the moment the car ploughed into pedestrians, he said: "He has gone straight through the red light at pace and it was bang, bang, bang. It was just one after the other."

John Stoupas, who owns Walker's Doughnuts on the corner of Flinders and Elizabeth Streets, said the car was travelling at around 50mph when it hit pedestrians as they were crossing the road.

He told the Guardian: "This is the busiest corner in Melbourne. This and Swanston Street corner are the two busiest corners in Melbourne. It was packed. Our store was packed.

"Pedestrians crossing the road were completely packed. It was solid with people. We were very, very busy in the whole area. All you could hear was the sound of the car hitting people [and] the screams."

The incident comes just the day after Victoria's Premier, Daniel Andrews, revealed plans to hold a public memorial for the victims of another alleged attack involving a vehicle in January.

Six people were killed and about 30 injured when a car hit pedestrians in Melbourne's Bourke Street – four blocks north of where Thursday's incident happened.

Melbourne resident Dimitrious Gargasoulas, 27, is due to face trial over the alleged attack. He has pleaded not guilty to six counts of murder.

Andrews described Thursday's incident as "an act of evil and an act of cowardice".

Police and emergency services attend to the scene of an incident involving a vehicle on Flinders Street, as seen from Swanson Street, in Melbourne, Australia December 21, 2017. Reuters