The 58-year-old was injured in the incident last night in St James's Road, Southsea, near to the University of Portsmouth's Eldon building.
Now police are hunting for a stocky white man, thought to be in his 40s, who was clean shaven and wearing a puffer jacket.
The victim is in a stable condition at Queen Alexandra Hospital in Cosham where she is undergoing treatment.
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A police cordon was in place this morning.
A Hampshire police spokeswoman said: ‘Investigations into the exact circumstances of what happened have been ongoing through the night and are continuing in the area today.
‘Officers are conducting house to house enquiries and checking local CCTV, so if you have any concerns or information, please speak to them.’
Anyone with information should call 101 quoting 44190415123.