A woman who tried to intervene during an argument in a Melbourne supermarket has suffered serious injuries after she was punched in the head.

St Kilda police are hoping to identify a man after a woman was punched in the head at a supermarket in Balaclava on October 30. Credit:Victoria Police

Police are now searching for a man following the alleged attack, which took place in a supermarket on the corner of Camden and Carlisle Streets in Balaclava, in the city's south-east.

The woman was in the line at the checkout about 7.45pm on October 30 when a verbal altercation broke out in front of her between a man and the sales assistant.

When the woman tried to intervene, the man punched her in the head.