Benitez, 27, joined the Middle Eastern club earlier this month from Mexican side Club America, after previous spells with El Nacional, Santos Laguna and Birmingham.
He was a regular for his country and made the Ecuador squad for the 2006 World Cup finals in Germany.
An Al Jaish statement on Monday confirmed his passing but did not give a cause of death.
It read: "The club would like to offer its sincere condolences to the family of the player.
"Benitez had recently joined the club from Club America for three seasons. The player participated for the first time with the team during yesterday's match against Qatar Sports Club in the Sheikh Jassem Cup without complaining of any health problems.
"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."
Source: PA
Source: PA