Staff at the Firhill Complex battled to save him after he collapsed on the pitch, according to an eyewitness.
Paramedics rushed to the centre near Garscube Road when the alarm was raised shortly after 8.30pm on Monday.
Paul McLaughlin, who was playing a match at the time, said: "We were on the park opposite and the next thing one of the guys shouted for anyone with first aid skills to go over.
"The man was being put into recovery position by his friends. There was panic as they tried to revive him.
"Staff came running over and a girl gave him mouth to mouth for about 15 minutes, until the paramedics arrived.
"It was pretty apparent quite early on that he was dead. We were in shock."
The man who died was part of a group of players who made a "regular booking", according to the centre manager, Gavin Duncan.
He said: "It's a tragic incident and we would like to pass on our condolences to his family.
"Everything that could have been done with what was available was done."
A spokesman for the Scottish Ambulance Service confirmed that they treated the man at the centre.
He added: "We sent a paramedic and an ambulance at 8.30pm to attend to a 40-year-old male who was taken to Glasgow Royal Infirmary."