The mangled wreckage of half a pram remains stuck on the bonnet of the car, while what appears to be the other half is further up the mall at a pedestrian crossing on William Street.
The baby who was inside it is believed to have died at the scene.
"A male deliberately drove into pedestrians in the Bourke St mall," police said.
Officers said the incident is believed to be linked to a stabbing of a man in Windsor, in Melbourne's south east at 2am on Friday.
The 26-year-old man responsible for the rampage in Melbourne's city centre on Friday has been identified as Dimitrious Gargasoulas.
The Melbourne resident has a history of mental health and drug-related issues and was charged with family violence offences last weekend.