A driver who smashed into a woman and a two-year-old girl at a Melbourne intersection asked whether they needed a doctor, but then returned to her car and sped away from the scene, leaving her injured victims on the road, police say.

Key points: The woman hit by the car is still in hospital with serious injuries

The woman hit by the car is still in hospital with serious injuries The two-year-old girl is still suffering from mental trauma over the crash

The two-year-old girl is still suffering from mental trauma over the crash Police are trying to enhance the CCTV to decipher the driver's numberplate

Police have released CCTV footage showing the moment the hit-and-run driver accelerated away from the crash scene, in the city's south-eastern suburbs.

Police said a black Toyota RAV4 was turning from Booran Road into Glen Huntly Road, in Glen Huntly, when it hit a 63-year-old woman and her granddaughter as they crossed the street about midday on February 20.

The woman suffered serious injuries including fractures to both her legs and broken bones in her hand. She remains in hospital.

The girl suffered bruising and mental trauma, police said.

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Watch Duration: 55 seconds 55 s Senior Constable Murray Stranger urges the driver to turn herself in

'She just got back in her car and drove away'

In the footage, the driver can be seen getting out of her car after hitting the pedestrians and walking towards them.

"The driver of the offending vehicle got out of her car and went and asked if they required a doctor and I suppose the people that were assisting assumed that she was going to ring for medical attention," Senior Constable Murray Stranger said.

"But as far as we know she just got back in her car and drove away."

The driver was described to police as Caucasian in appearance, aged in her 40s or 50s and about 160 centimetres tall.

Senior Constable Stranger said police were "very confident" they would be able to enhance the CCTV footage and read the numberplate of the car involved.

The girl's mother, Laura, said she bore no malice towards the driver but would like them to turn themselves in.

"It perplexes me how that can happen or how someone could do that … I do understand that people make mistakes, everyone does, but it's time to do the right thing," she said.

Laura said her daughter was still mentally recovering from the crash. ( ABC News )

She said her mother had been taking her daughter to buy an ice cream at the time, after they had spent time in the park.

Laura said she felt "so grateful" her daughter had been shielded from the brunt of the crash and was not badly injured.

But she said her daughter was more fearful around cars and sometimes mentioned the crash in conversation.

Driver told to 'have a conscience'

Senior Constable Stranger also urged the driver to come forward before police located her themselves.

"Obviously if she presents herself now to us, it's going to go much better in the eyes of the law that she actually did have a conscience and come forward and present herself to us," he said.

Police are urging anyone with information to contact Crime Stoppers on 1800 333 000.

Under Victorian law, drivers who fail to stop and help after a crash that has injured someone can be fined $140,000 and face jail terms of up to 10 years.

The release of the footage comes days after a cyclist was killed in a separate alleged hit-and-run in the city's south-east.

A 50-year-old woman was cycling along the Nepean Highway on Thursday when she was hit by a ute, which police alleged failed to stop.

She was taken to hospital in a critical condition but died on Sunday.

A 28-year-old Parkdale man was charged over the incident.