The victim was walking in Greendyke Street at about 2200 BST on Monday when she was approached by the attacker.
As she entered Glasgow Green and made her way to the River Clyde Tidal Weir the man struck her on the head and indecently assaulted her.
Strathclyde Police said the suspect was aged 40-45 and had two or three fingers missing from one hand.
Badly shaken
Police also said he was thin, 5ft 7ins to 5ft 9ins, with grey spiky hair and was wearing a denim jacket, jeans and a black belt.
He was also wearing a chain with a cross around his neck.
The woman was badly shaken as a result of the incident but did not require hospital treatment.
Detective Constable Ross Arnott said: "I would appeal to anyone who recognises the description of the suspect to contact my office where information can be given in confidence."
Anyone with information should contact London Road police office on 0141 532 4600 or Crimestoppers on 0800 555 111.
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