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The club provided no further details about the death of the 27-year-old Benitez, who moved from Mexican club America to play in Qatar this year.
"The club would like to offer its sincere condolences to the family of the player," the club said in a statement. "His sudden departure is a big shock for each member of the technical and administrative staff. He was a player that over the short period he was here was regarded for his high moral character."
El Jaish played Qatar Sports on Sunday in the Sheik Jassim Cup, a warm-up tournament for the upcoming football season. Benitez, who also spent a season in England with Birmingham, was in the lineup.
The match was played in hot and humid conditions, which are typical of the Persian Gulf at this time of year.
"The player participated for the first time with the team during yesterday's match against Qatar Sports Club in the Sheik Jassim Cup without complaining of any health problems," the club said, adding that it was awaiting results from a medical report that could be released later Monday.
A powerful, destabilizing striker, Benitez was the Mexican league's top scorer last season and helped his team win the championship.
The Mexico City-based America is one of the country's most popular teams.
"The Club America football team deeply regrets the death of one of the most recent America idols, and shares the sorrow felt by the entire Benitez Betancourt family, and the sport in Mexico, Ecuador and the world," the club said on its website.
Qatar will host the 2022 World Cup and the searing temperatures have prompted many former football stars as well as FIFA President Sepp Blatter to call for the competition to be moved to the cooler, winter months. Blatter plans to ask FIFA's executive committee later this year to move it.
