Castro was placed on the 15-day DL due to a right quad strain he suffered Friday night. Stassi joined the team Saturday in Minnesota.
Castro, 28, has played in 90 games this season, batting .220/.284/.395 with 11 home runs and 30 RBIs. Conger has hit .218/.322/.435 in 53 games, with eight home runs and 21 RBIs.
The Astros entered Sunday with a four-game lead over the Texas Rangers in the AL West.