The boy was taken to Queen Elizabeth University Hospital by ambulance following the incident, which took place on Aitkenhead Road just before the semi-final kicked off around 2pm on Sunday.
His injuries are not thought to be serious and he is expected to be released soon.
A Police Scotland spokeswoman said: “Around 1400 hours on Sunday, October 23, an 11-year-old boy sustained a head injury after being hit by a bottle whilst walking along Aitkenhead Road, Mount Florida.
“He was taken by ambulance to the Queen Elizabeth University Hospital for treatment.
“Details of the seriousness of any injury is not know at this time but it is not thought to be serious.
“Inquiries into the incident are ongoing.”