The incident happened when two men were standing in the lane near Asda in Gorstan Street, Summerston, at around 9.10am yesterday.
Another man app-roached them and began speaking to them.
He then attacked one of the men, punching him and hitting him in the face with a hammer before running off towards Arrochar Street.
The 35-year-old victim was taken to Glasgow's Western Infirmary for treatment before being released.
The suspect is white, around 5ft 9in with a stocky build. He was clean shaven and wearing a black hooded top with yellow stripes and a yellow logo on the front.
Detective Sergeant Lesley Ann McGee said: "The victim has had to have treatment for a facial injury after this man lashed out for no apparent reason.
"We will be checking CCTV images from the area in an effort to find out more about the suspect.
"This is a busy area and there would have been a lot of people around at the time of the crime.
"Although the suspect was wearing a dark top, it did have bright yellow stripes and a yellow logo which people may remember seeing.
"I am appealing to anyone who may have any knowledge regarding this incident to get in touch."