A white SUV showed no signs of slowing as it mowed down a number of people at the busy intersection.

Police have arrested the driver of the Suzuki SUV.

An officer at the scene has described it as a terrorist incident, but this has not been confirmed.

It appears police have not enacted counter-terrorism lock-down strategies. The new terror warning sirens have also not been activated.

Police have confirmed the car was not travelling at high speed when it collided with the pedestrians.

The pedestrians were struck in front of dozens of people as they crossed the busy intersection at the beginning of peak hour.

One distressed woman carrying Christmas presents and wrapping paper could be seen crying as police escorted her into an unmarked police car.

Sections of the city's public transport system are in lock-down with Metro Trains urging commuters to avoid Flinders Street. 

"Due to a major incident at the intersection of Elizabeth and Flinders Streets, passengers are advised to defer travel through Flinders Street Station," Metro Trains tweeted. 

"Please interchange for services at Southern Cross and City Loop Stations."

A pre-school aged child is among the injured and has been taken to the Royal Children's Hospital in a serious condition with head injuries.

Paramedics are assessing 12 people at the scene. Up to seven have been taken to hospital: three to The Alfred and three to the Royal Melbourne. Their injuries and condition are not yet known.

Officers were holding up tarps around some victims.

Police said investigators were still piecing together how the incident occurred and were calling for witnesses to immediately come forward.

"Police have saturated the CBD area in the vicinity of Flinders, Elizabeth and Swanston streets to ensure community safety," Victoria Police spokeswoman Creina O'Grady said.

 "A number of people are being treated at the scene for a range of injuries."

People working nearby have been left shaken by the incident with some businesses including Boost Juice on Elizabeth Street closing for the day. 

Sue from Walker's Doughnuts on Elizabeth Street told radio station 3AW that she heard screams before she saw "people flying everywhere".

"We could hear this noise, as we looked left, we saw this white car, it just mowed everybody down," she said.

"People are flying everywhere. We heard thump, thump. People are running everywhere."

Rohit Kaul, 45, was on the phone to his wife Avi and crossing the intersection at Elizabeth Street when he was mowed down by the car.

Mr Kaul heard the loud noises down the line before her husband's phone cut out and she unsuccessfully tried calling him several times.

He sustained leg injuries and was helped by several pedestrians who had been walking in front of him and managed to return his wife's call.

He has been transferred to The Alfred hospital.

Police have blocked off Flinders Street from Queens Street to Swanston Street and are not allowing pedestrians through.

Hundreds of people are milling around the edges of the crash scene with police quelling a group in the crowd calling out that the incident was a terrorist attack.

A heavy police presence rushed to the scene just before 5pm on Thursday. 

Footage from the scene shows crowds of scattered people surrounding the white SUV in the middle of the intersection. 

Dozens of police cars, fire trucks and ambulances have descended on Flinders Street.

Police are asking any witnesses to go to the Melbourne West Police Station at 313 Spencer Street, Melbourne and all vehicular and pedestrian traffic to avoid the area. 

They have appealed to any members of the public who have video or images of the incident which can assist with the investigation to upload them here.