Officers were called to reports of an altercation between two men on Shakespeare Avenue in the town at about 01:50 on Sunday.
The injured man was taken to the Queen Elizabeth University Hospital.
The suspect was believed to have been carrying a weapon. He was described as wearing a black hooded top and black trousers.
Detective Constable Bruce Fyfe from Clydebank CID said: "Inquiries are ongoing to establish the circumstances surrounding how this man came about his injuries.
"Officers are currently examining CCTV footage to try and trace the suspect and I would ask anyone who saw a man matching the description in the area around the time of the incident to get in touch."
Police have appealed for information after a man suffered serious facial injuries in an attack in Clydebank.