The trouble involved two groups of men outside the Millennium Hotel on North Hanover Street at about 19:45.
Emergency services attended and two men, aged 45 and 53, were taken to the Glasgow Royal Infirmary for treatment to serious head injuries.
Medical staff describe their conditions as stable. Police are appealing for witnesses to contact them.
Det Con Tara Hogan said: "I would appeal to anyone who may have witnessed the disturbance to please come forward as you may be able to assist with our inquiries."
Two men suffered serious injuries when fighting broke out in Glasgow city centre on Saturday evening.