Weiland has bursitis in his right shoulder. His stint on the DL is retroactive to Wednesday.
The 25-year-old is 0-3 with a 6.62 ERA in three starts for Houston this season. He joined the Astros in an offseason trade with Boston.
Gonzalez has hit .231 in 16 games this season. He can be on the paternity list for up to three days.