A woman has been charged over an alleged hit-and-run that left a 13-year-old girl fighting for life in Melbourne's north.

A 41-year-old Sunshine North woman handed herself in at the office of her lawyer in the CBD about 11:00am.

She has been bailed to appear at Melbourne Magistrates' Court on Monday, charged with dangerous driving causing serious injury, failing to stop after a serious injury collision, failing to render assistance after a serious injury collision and failing to exchange name and address or report a collision.

The girl was hit by a dark BMW while she was riding her bicycle near the corner of Bell and Sussex streets in Coburg, just after 8:00pm on Sunday.

The 41-year-old Sunshine North woman leaves court after being charged. ( ABC News )

She was placed in an induced coma and remains in a critical condition after sustaining head injuries and broken bones.

"We are hoping that there are small signs of improvement but of course it's a long way away before we're in a position to say she will recover," Victoria Police Detective Inspector Stuart McGregor said.

"We are just crossing our fingers that she will survive and she will recover."

The BMW police believe hit the girl was seized on Monday. ( Supplied: Victoria Police )

After a two-day search, police seized a dark grey BMW believed to have been involved in the hit-and-run in Braybrook, in Melbourne's west, on Wednesday.

Investigators had urged the driver of the car to come forward on a number of occasions.

They had also been keeping a close watch on airports to monitor who was leaving the state.