The 24-year-old striker was taken to a nearby hospital from the stadium in Guimaraes after falling to the ground in injury time.
Medical personnel struggled to save him for about 90 minutes "until about 11:10 p.m., without success, the player having died", the spokesman told private radio station TSF.
Television reports said that emergency medical personnel had managed to revive Feher on the field using a defibrillator. However, his heart had stopped by the time he reached hospital. An autopsy is scheduled for Monday.
This was the second on-the-field death of a professional soccer player within seven months.
Cameroon midfielder Marc-Vivien Foe died in June when he collapsed during a Confederations Cup semi-final against Colombia in Lyon in France. He was suffering from a heart-related condition.
The stadium in Guimaraes, about 320 km north of Lisbon, will be one of 10 hosting the European soccer championship finals this summer.
TSF radio announcers at the game spoke of a delay in the arrival of the ambulance but Domingos Gomes, a UEFA doctor, told RTP state television that despite "access difficulties" impeding the ambulance Feher had received adequate care. "Everything was quick," Gomes said.
Asked by TSF about the apparent delay in the ambulance's arrival, Gilberto Madail, chairman of the Portuguese Soccer Federation, said the dispatch of an ambulance was uncommon. He said Benfica personnel normally could deal with a heart attack.
"I don't know, but I presume that an ambulance would only enter when the doctors attending the player asked for it to come in," Madail said.
Feher had come on as a substitute after 60 minutes.
He bent over and then fell on his back. Team mates rushed to his side and one cradled his head.
When team medics tried to revive him, some Benfica players kneeled to pray while others were crying, including coach Jose Antonio Camacho.
Feher came to Portugal to play for Porto in the 1998/99 season from Hungary's Gyor Eto. He was traded to Benfica in 2002/03 season after being lent to Salgueiros and Braga.
