A driver for the popular ride-sharing service Uber has been arrested over allegations he indecently assaulted a Melbourne woman on a drive on New Year's Day.

The woman, 19, booked the car through a mobile phone application and was collected on King Street about 4am, police spokeswoman Belle Nolan said.

It was alleged the woman was indecently assaulted during the trip before she was dropped off at a Templestowe address, Ms Nolan said.

It was there the matter was reported to police, she said.

Detectives from the Box Hill sexual offences and child abuse investigation team arrested the driver, a 31-year-old Noble Park man, on Saturday.