A search is underway for a swimmer who has gone missing at Mornington, south-east of Melbourne.

Lifesavers from the Mornington Life Saving Club saw the woman floating on her back about 150 metres from the shore at Mills Beach about 9:30am (AEDT).

She has not been seen since.

A search of waters in the Mills Beach and Red Bluff area has so far failed to find her.

Several other people had to be rescued from a nearby rip this morning.