The woman was struck by a car, which was backing up Flinders Street near Highlander Lane, around 9:30 am, sustaining life-threatening injuries.
Police arrested the driver of the vehicle, a 33-year-old Caulfield man, at the scene.
He remains in custody and is assisting the police with their investigations.
Detective Sgt. Peter Romanis says police are investigating why the driver backed up the busy street about 100 feet before hitting the pedestrian.
“The driver of a Mazda CX-5 was backing up Flinders Street and struck a pedestrian crossing the street,” he said.
“As for the reason why he was backing down, it is currently unknown.
“We haven’t been able to determine the motive. We hope he can shed some light on that.”
There have been 17 pedestrian fatalities in Victoria since the start of the year and Romanis urged drivers to pay attention.
“It is concerning that we are seeing an upward trend in pedestrian fatalities,” he said.
“We urge all road users to be vigilant, watch out for each other and motorists to pay attention to all pedestrians.”
Flinders Street is closed to the east, between King and William streets, due to the incident.
Streetcar services on routes 70 and 75 have resumed normal service, after a brief interruption.
The pedestrian has been taken to Royal Melbourne Hospital, where she remains in critical condition.
Witnesses or anyone with dash cam footage of the incident are urged to contact police.