Police said a 28-year-old was seriously assaulted within the stadium at around 7.45pm on Tuesday, just as Celtic were kicking off against Kilmarnock in a Betfred Cup tie.
The incident reportedly took place within a hospitality suite.
The victim was taken to Glasgow Royal Infirmary for treatment to a facial injury.
No-one has been arrested but police are following a positive line of inquiry.
Celtic FC said they are aware of the incident, which is now in the hands of police.
A Police Scotland spokeswoman said: “Police inquiries are ongoing after a 28-year-old man was seriously assaulted within Celtic football stadium, Glasgow, around 7.45pm on Tuesday August 8.
“The injured man was taken by ambulance to Glasgow Royal Infirmary where he is being treated for a facial injury. Hospital staff describe his condition as stable.”
A Celtic spokesman said: “We are aware of an incident taking place and the matter, which is not football related, is now in the hands of Police Scotland.”