The Ecuador international, nicknamed 'Chucho', signed for Qatari club Al Jaish less than a month ago.
He was admitted to hospital with severe stomach pain hours after making his debut against Qatar Sports Club in the Sheikh Jassem Cup, but died shortly afterwards.
"This morning we woke feeling profound pain, a pain that all Ecuadorians share, after losing an extraordinary human being, a son, friend, husband and player, " Luis Chiriboga Acosta said in a statement on the FEF's official website on Monday.
The FEF president explained the Federation would charter a flight to return the deceased player's body to Ecuador along with his wife, adding that some Ecuador players, including Manchester United winger Antonio Valencia, had committed to helping with the process.
Chiriboga also announced that the main pitch at the national team's training ground would be named after Benitez.
Benitez joined Al Jaish earlier in July from Club America, after previous spells with El Nacional, Santos Laguna and Birmingham.
An Ecuador Football Federation (FEF) statement read: "The FEF regrets to inform you of the death of Christian Benitez, the striker of Qatar club Al Jaish and the Ecuador national team.
"Benitez, who was with his new club in Qatar, had a severe stomach pain, which was why he was rushed to a hospital, where after a few hours he suffered a cardiorespiratory arrest, which ended his life.
"The Ecuadorian Football Federation extends its heartfelt sympathy to the family - parents, wife, children - and friends of our striker Christian Benitez.
"May he rest in peace."
Benitez was a regular for his country and made the Ecuador squad for the 2006 World Cup finals in Germany.