The assault happened at 5.25am on Tuesday at George’s Wee Dairy in Clarendon Street, Maryhill.
Police say two men tried to steal the till but were unsuccessful. They then stole a quantity of cigarettes and other store items.
The 62-year-old victim was taken to Glasgow Royal Infirmary after suffering a head injury. He has since been released from hospital.
Police say the first suspect was white, about 5ft 8ins to 5ft 10ins and of medium build.
He was wearing a dark green hooded top, with the hood up and a red top underneath. He also wore a padded style dark green jacket.
The second man was white, about 5ft 8ins to 5ft 10ins and slim. He was wearing a black hooded top with the hood up.
Both men are described as being in their late teens.
Officers have been carrying out door-to-door inquiries in the area and are gathering CCTV footage for review.
In a separate incident in North Ayrshire, a man was seriously assaulted outside a petrol station.
Police say the attack happened outside the Ardeer Filling Station on Saturday March 10.
The 20-year-old suffered a head injury and required hospital treatment in the assault at 4.30am.
The suspect is described as being a white man in his 20s with medium build and brown hair.
He was wearing a dark top, grey trousers and dark trainers.
Detective Constable Jennifer Carruth, of North Ayrshire CID, said: “This attack has left the victim badly injured and inquiries are under way to trace the person responsible.
“Extensive inquiries have already been conducted, both from officers attending door to door and reviewing CCTV of the area, however I would appeal to anyone who was in the area during the early hours of Saturday March 10 and witnessed a disturbance or anything suspicious to please get in touch.”
Anyone with information on either of the attacks is asked to contact Police Scotland on 101.