The incident took place in North Street, close to Charing Cross, shortly before 03:00.
The man was taken to Glasgow Royal Infirmary before being transferred to Queen Elizabeth University Hospital for treatment.
Medical staff described his condition as serious.
An area of North Street was closed off by police following the incident. Police said they had no description of the suspect.
Det Sgt Kevin Browne said: "From our early inquiries, this was an unprovoked attack on a man making his way home from a night out.
"The 42-year-old man was punched by another man who then made off in the direction of Sauchiehall Street.
"Our inquiries have been continuing through the night. Officers remain at the scene.
"We have been analysing CCTV and speaking to people who were in the area following the incident.
"At this time, we are seeking information from anyone who has information which can help trace the man responsible."
A 42-year-old man was seriously injured after being punched in an "unprovoked" attack in Glasgow city centre during the early hours of Saturday morning.