A cyclist has been seriously injured and is fighting for life after he was hit by a car in Melbourne's south-east.

Police believe the man was riding along the Nepean Highway when a silver Honda Jazz hit him near Union Street, Brighton East, about 9.30pm on Tuesday. The driver did not stop at the scene.

Ambulance Victoria spokesman Paul Bentley said the cyclist, aged in his 50s, suffered serious head injuries and paramedics stabilised him at the scene.

He was taken to The Alfred hospital in a critical condition.

A 31-year-old woman was later arrested at a house in Moorabbin, and she is helping police with their inquiries.

Anyone with information is asked to phone Crime Stoppers on 1800 333 000 or visit www.crimestoppers.com.au.