The move was announced on Friday before Minnesota's interleague game at the Chicago Cubs.
Punto went on the DL on May 29 with a strained right groin. The switch-hitter has been a valuable utility player for the Twins since 2005. He was batting .187 at the time of his injury, well below his .284 average last season.
Casilla was batting .180. Neither player had homered this season.