A Ferrari has been destroyed and several people escaped injury after the driver of the luxury car smashed into a taxi in Melbourne's CBD.

The cars collided at the intersection of Elizabeth and Collins Streets around 3:00am (AEST) and the Ferrari ended up on the footpath.

It is believed at least one pedestrian was forced to jump out of the way as the car ran up the curb.

The driver fled the scene and the owner of the Ferrari arrived some time later, inspecting the damage as the car was loaded onto a tow-truck.

Two women travelling in the taxi were unhurt but shaken.

Sergeant Matt Griffiths said police are investigating reports the driver of the Ferrari ran a red light before the crash.

"[There are] a lot of 'what if' questions. It was very, very lucky that everyone got out, that no-one was badly hurt," he said.

"It's a timely reminder that it's a 40 zone in the city and a moment's distraction here in the red light could have resulted in fatalities or serious injuries."

Sergeant Griffiths said he was glad he did not have pay for the repairs to the vehicle.

"I would suggest that's going to be a terribly expensive repair bill," he said.