A three-month-old baby has died in hospital a day after a man with a history of mental health and drug issues drove a car through a lunch-time crowd in a pedestrian-only street in Australia's second largest city.

The fifth victim of the attack died in hospital late on Saturday and four people remained in hospital in a critical condition after a stolen vehicle caused havoc in central Melbourne on Friday, police said.

The driver, Dimitrious Gargasoulas, 26, remained in hospital after being shot in the arm by police who captured him at the scene in Bourke Street. His wound was not life-threatening.

The incident came amid global concern over extremists using vehicles to strike crowds, following truck attacks in Berlin and Nice, France, last year, but police said there was no link to terrorism.

Police hope to interview and charge Gargasoulas in hospital on Sunday.

He was one of 37 people who received hospital treatment as a result of the incident.

Police had been looking for Gargasoulas since he stabbed his brother Angelo Gargasoulas early on Friday. The brother was critically injured and remained in hospital.

Police had called off a pursuit because of Gargasoulas's dangerous driving before he drove into Bourke Street.

A 10-year-old girl, 25-year-old man and a 32-year-old woman died at the scene. A 33-year-old man died in hospital on Friday night.