Souza, acquired from Tampa Bay in a three-team trade in February, opened the season on the DL with a strained right pectoral. He returned on May 3 but reinjured the pec and was put back on the DL on May 22.
Souza was in right field for Thursday night's series opener against San Diego.
Dyson was injured in Arizona's loss to St. Louis on Wednesday night.
The Diamondbacks also recalled right-handed reliever Silvino Bracho from Triple-A Reno after optioning right-handed reliever Kpey Krehbiel to Reno following Wednesday night's game.