A woman was hospitalised with a fractured skull and police have a mystery on their hands after a golf ball rocketed through the open window of a taxi at 2am in Melbourne's south-west.

The 38-year-old Sanctuary Lakes woman was in the front seat of the cab with her window down on Sanctuary Lakes Boulevard, Sanctuary Lakes, on February 28, when the ball struck her temple.

The ball was travelling with such force it fractured her skull.

A police spokeswoman said it was unknown from where the golf ball had come. Investigators did not know if it was from the nearby golf course, from a back yard or somehow ''fired into the air'' by local kids.

The woman was taken to Werribee Hospital and later rushed to St Vincent's Hospital where she was treated until being released last night.

Police, who said they do not know how the golf ball ''took flight'', are appealing for anyone with information about the incident to come forward.

Anyone with information can call CrimeStoppers on 1800 333 000 or go to crimestoppers.com.au.