The victim was set upon by two young men in the city's Renfield Street KFC at around 11pm on Friday.
Detectives hunting the attackers said it was a "particularly violent" assault. The victim and his friend were confronted by three men and a woman while standing in the queue and, as they tried to leave, two of the men attacked the 28-year-old man.
The attackers, both white and aged 18 to 20, were last seen in Bath Street. The first suspect is described as slim with dark hair. He was wearing a grey tracksuit with yellow writing on it. The second man wore a dark jacket and had the name Scott tattooed on the right side of his neck.