Ambulance services were called to the car park on Racecourse Road shortly after 7:30pm on Friday after a report that a man was unconscious in a car.
When paramedics tried to wake the man, police said he rammed his white Infinity sedan into the ambulance several times.
The man also hit two other vehicles before driving off west along Racecourse Road.
No-one was injured.
The car believed to have been involved in the incident was found near Domain Road in South Yarra this morning, police said.
Police said they were investigating if the car had been stolen from Carlton.
They said said no one had been arrested.
Anyone with information has been asked to contact Crime Stoppers.