Police allege a man stole the ute from a business in York Street, South Melbourne, about 11am following an aggravated burglary.

The ute then hit a parked vehicle on the same street, before careering into a roundabout and losing a wheel.

It then slammed into an unmarked police car on Cecil Street, before heading along the tram tracks on Clarendon Street and hitting a second unmarked police vehicle outside Crown Casino.

Two police officers were inside the unmarked van and were taken to The Alfred hospital with serious but non-life threatening injuries. The ute was not being pursued by police at the time of the incident, a police spokeswoman said.

The driver was arrested at the scene and taken to hospital with minor injuries.  Police believe the driver was responsible for an aggravated burglary earlier in the day.

"Investigators are calling for a driver who was side-swiped by the stolen white ute in York Street around 11am to contact police," the spokeswoman said.

The injured officers, from a special operations unit, were not aware of the driver's history at the time, police said.

Other police officers who were called to the crash scene recognised the suspected burglar.

The incident blocked Clarendon Street for several hours, causing delays for motorists and tram commuters.

Police investigations are continuing.

Anyone with information is asked to contact Crime Stoppers on 1800 333 000.