The 22-year-old man was rushed to hospital after falling in a stairwell of Glasgow's Celtic Park.
Police Scotland and the Scottish Ambulance Service attended the scene at exit 33 of the ground and the man was transferred to Glasgow Royal Infirmary where he later died.
A police spokesman said: "Relatives have been informed and the Health and Safety Executive have been made aware.
"There are no suspicious circumstances and a report will be prepared for the procurator fiscal."
Scotland won 1-0.