The 22-year-old Spanish international had been in a critical condition in the Virgen del Rocio hospital in Seville since being admitted on Saturday. The hospital confirmed his death.
Sevilla said that Puerta's body would be taken to the club's Sanchez Pizjuan stadium where fans could pay their respects and that the player would be buried on Thursday.
The player was due to become a father in under two months, Spanish media reported.
Puerta's condition has completely overshadowed the Sevilla squad's preparations for the Champions League third qualifying round second leg against AEK Athens in Greece on Tuesday.
The club's radio reported that UEFA had agreed to postpone the game and the Spanish Football League also called off the league game at Osasuna on Monday.
An AEK spokesman said the Champions League tie would be played on Monday Sept. 3.
AC Milan, Sevilla's opponent in Friday's European Super Cup, expressed its condolences at the player's death, saying it was prepared to call off the game if necessary.
"AC Milan ... grieves at the passing of Antonio Puerta and share the pain of our friends at Sevilla and the player's family," the club said in a statement. "Milan is ready to stand by any decision adopted by UEFA about the playing or not of the European Super Cup.
Puerta collapsed after jogging back towards his own goal 35 minutes into the game against Getafe at the Sanchez Pizjuan on Saturday night.
Teammates and medical staff immediately rushed to his side and were seen preventing him from swallowing his tongue as he lost consciousness, but he was able to walk from the pitch.
Doctors said that he collapsed again in the changing rooms and had to be given cardiac resuscitation before being taken to hospital.
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22 años, joder.