The game had kicked off as planned but was halted early in the first half, with local media later confirming a 64-year-old Granada supporter had passed away after suffering a cardiac arrest.
LaLiga have since announced that the match will restart on Monday from the 17th minute, with Athletic leading 1-0 thanks to an early strike from Iñaki Williams.
"Granada vs. Athletic Bilbao was suspended following the tragic death of a fan at the Estadio Nuevo los Cármenes," the league said.
"Our condolences go out to their family and friends, as well as to all Granada fans.
"At the request of LaLiga, the RFEF competition judge has ruled that the fixture will resume on Dec. 11 at 9pm. The match will restart from the 17th minute."
Fans had started chanting for the ball to be put out of play as the gravity of the situation became known in the first half, with the players then leaving the pitch.
After an hour of paramedics working to resuscitate the fan, LaLiga announced that they had died and that the game had been suspended, with both clubs in agreement with the decision.
"LaLiga and the two clubs have all agreed to call off the match due to the death of a fan at Los Cármenes," Athletic said on social media.
"Athletic Club expresses its deepest condolences. Our thoughts are with the person's family and loved ones."