The death toll from an incident on Friday afternoon in which a car was allegedly deliberately driven at pedestrians in central Melbourne has risen to five with more than 30 people injured.

Police have said those who have died include a 10-year-old girl, a 25-year-old man, a 33-year-old women and a three-month-old baby boy who died in hospital on Saturday night. They said 37 people were treated in hospital.

Police were in pursuit of a car in the CBD at about 1.30pm Friday when the driver allegedly deliberately ran down a number of pedestrians after driving through the Bourke Street Mall and then along footpaths in Bourke Street until police rammed the vehicle. 

A 26-year-old man was arrested. Police have said the incident wasn't terrorism-related.

People have been laying tributes in the Melbourne CBD where a makeshift memorial has been established at the corner of the Elizabeth and Bourke Streets. A vigil is being planned which will be held in Federation Square. Donations to aid those families who lost loved ones can be made at www.vic.gov.au/bourkestreet.html.