Police say they were made aware of a concern for a woman within toilets in the stadium shortly after 2.30pm on Saturday, April 13.
Emergency services then attended, however, a 54-year-old woman was sadly pronounced dead at the scene.
Officers have since confirmed the death is not being treated as suspicious.
A report will be submitted to the Procurator Fiscal.
A spokesperson for Police Scotland said: “We were made aware of concern for a woman within toilets at Celtic Park in Glasgow around 2.45pm on Saturday, April 13.
“Emergency services attended but the 54-year-old woman was pronounced dead at the scene.
“The death is not being treated as suspicious and a report will be submitted to the Procurator Fiscal.”
The Scottish Ambulance Service and Celtic Football Club have been contacted for comment.
