A pedestrian has been injured in a hit-and-run incident involving an allegedly stolen vehicle in Melbourne's CBD, near Queen Victoria Market, Victoria Police say.

The incident, which police said was not terrorism-related, happened on A'Beckett St near Queen Street.

Police tried to stop an allegedly stolen car driving on Flinders Street about 5:00pm and the car took off.

Witness Troy Naismith said the silver car hit the gutter, as well as other cars, before knocking over a traffic light, which then hit a pedestrian.

Fire officers look at the crash scene in Melbourne's CBD. ( AAP: James Ross )

"He came up the gutter here, ping-ponged, hit the sign there, he hit a few cars on the way up, hit the traffic lights, knocked the traffic light over, which hit another bloke, hopped out of the car and ran up to Queen Street," he said.

"It looked like he was deliberately running away but it didn't look like he deliberately hit someone."

The driver — a man — and a male passenger then fled on foot.

One person was taken to hospital with serious but not life-threatening injuries. ( AAP: James Ross )

The driver is described as being Caucasian, about 183 centimetres tall, with his hair tied back and wearing a high-vis top.

The passenger is believed to be in his 20s or 30s, Caucasian and wearing a grey top.

The pedestrian was taken to The Alfred hospital with serious but non-life threatening injuries.

Staff in a nearby restaurant said they heard a loud bang and saw a pedestrian lying on the pavement.

A witness said the car hit a traffic light and lost control, mounting the footpath. ( ABC News: Joseph Dunstan )

Another witness, Doug (surname withheld), said he heard an "almighty noise" coming from behind him before the pedestrian was hit.

"I turned around and I saw this car coming at a high rate of speed with the bumper bar hanging off the front of it," he said.

"Bits and pieces of the car were flying everywhere.

"Cars were parked, waiting at the lights and he just ploughed straight through them. Knocked the cars, obviously knocked the traffic lights over and a poor pedestrian."

Doug said he initially thought the pedestrian had died because he was lying face down.

"It was very traumatic," he said.

There was a second, unrelated incident nearby on Market St, in which a traffic light was struck, injuring another pedestrian.