Officers are appealing for witnesses to the attack, which happened last weekend.
They say the woman was walking along the footpath which links Staithe Road and Caius Close, between midnight and 12:10am on Sunday, February 23, when she approached a man and a woman arguing.
As the victim tried to pass the couple she was struck in the face by the man and fell against a wooden bollard. The victim received a broken thumb and a cut lip as a result of the incident.
The male suspect is described as white, 6ft tall and of slim build. He was wearing a black hood top at the time of the incident. The woman he was arguing with is described as white and around 5ft tall. She was wearing a dark parka style coat with a fur rimmed hood.
Anyone who saw the incident or has any informatrion about it is asked to call PC Dave Ringwood, at Hunstanton police station, on 101.
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