The 43-year-old man was seriously assaulted in the Calton area in the early hours of Sunday.
He was walking along Bain Street, towards the Gallowgate junction, at about 1am when he was struck on the head by a bottle.
The man did not see who threw the bottle. As it struck him, he fell to the ground. A woman then went to help him.
He was later taken to hospital and discharged after treatment.
Officers are making inquiries and are gathering CCTV film in an effort to obtain further information.
Police would like to speak to the woman, who was believed to be aged 30-48 and about 6ft with long straight dark hair.
Detective Constable Cameron MacLean said: "This man was walking along the street when he was struck by a bottle for no apparent reason.
"I would like to speak to the woman who helped the victim and I would appeal to her to contact police. She may have seen something that could assist our inquiry.
"If anyone knows anything about the incident or who may be responsible, I would ask them to call us."
Anyone with information is asked to call London Road police office on 0141 532 4600 or Crimestoppers, anonymously if desired, on 0800 555111.