Emergency services confirmed they are at the scene.
'Paramedics have now transported 13 people to city hospitals. Two more people are being assessed by paramedics at the scene,' Ambulance Victoria said in a tweet.
‘A pre-school aged child with a head injury has been taken to RCH in a serious condition,’ the organisation said in a statement.
'One person has been taken to The Alfred hospital, injuries and condition unknown.’
Victoria Police said the incident involved a vehicle colliding with a number of pedestrians.
'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,' Victoria Police tweeted just after 5pm.
‘Police have arrested the driver of the car,’ they said.
'If members of the public have video or images which might assist police with their investigation into the Flinders Street incident they are encouraged to upload them here,' the police continued.
The incident occurred on the corner of Elizabeth Street and Flinders Street at 4.41pm on Thursday.