The Elmore County Sheriff's office says the three were fishing Sunday afternoon in southwest Idaho when the men went in after the boy and were swept away by the current.
A 23-year-old man also jumped into the river and was able to rescue the boy.
But witnesses told deputies that the two men both disappeared under the surface before anyone could reach them.
The department says in a release that divers pulled them from the water, but they were pronounced dead.
They were identified as 37-year-old Jose Jorge Barroso-Alfaro and 35-year-old Martin Barroso-Alfaro, both of Mountain Home. The release didn't identify which was the father or provide further details of their relationship.