Aldo Sarabia, part of the brass section of the 18-member group, was reported missing by his band mates last week.
Sinaloa State Prosecutor Marco Antonio Higuera Gomez said Sarabia's wife, Alma Delia Chavez Guerrero, and her purported lover, Yahir Alfredo Sandoval, met about four months ago.
The prosecutors said that the day after Sarabia returned from a recent tour, Chavez invited her husband to dine at a seafood restaurant.
Higuera Gomez said the suspects could face 30 to 50 years in prison if convicted.
Sarabia's body was discovered yesterday in the neighbourhood of El Recodo, which has the same name as the band.
The body had at least one gunshot wound and was in a state of decomposition, said an official at the Sinaloa state prosecutor's office.
The official, who was not authorised to discuss the case, agreed to reveal the information only on condition of anonymity.
Banda El Recodo is popular in Mexico and the United States and has won multiple Latin Grammys.
"Aldo Sarabia Garcia is now in heaven," it said. "He was our companion and inspiration in a thousand battles, and all the moments we shared will endure in the hearts of those of us who knew him."
The statement called him a great friend and father.
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