A woman has been left with an eight centimetre gash across her neck after she was robbed and assaulted while shopping during the mid-afternoon in St Kilda.

The woman, in her 30s, was walking near a laneway at Inverleith Court about 3.30pm when she was approached by a man she didn't know.

Port Phillip Crime Investigation Unit detectives are hoping to identify a man after a woman was robbed and assaulted with a knife in St Kilda last month. Credit:Victoria Police

He demanded she give him her purse, but she refused.

The man then produced a small cutting knife and slashed the woman on the neck.