The Qatari club El Jaish provided no details about the death but said Benitez did not complain about his health Sunday. The team is awaiting a medical report.
El Jaish played Qatar Sports in the Sheik Jassim Cup, a warmup tournament for the upcoming season. The team said this was Benitez's first game with his new team.
The game was played in hot and humid conditions typical of the Persian Gulf this time of year. Qatar will host the 2022 World Cup and the searing heat has prompted many in soccer to call for the tournament to be moved to winter.
Benitez, a powerful striker, joined El Jaish after helping his Mexican club America win the championship last season.
"He was a player that over the short period he was here was regarded for his high moral character," El Jaish said in a statement.
Benitez also spent a season in England with Birmingham. In Mexico, he played with one of the country's most popular teams. On its website the team mourned "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."