Oswalt left Tuesday's win over the Chicago Cubs at Wrigley Field in the second inning with a strained lower left back. He flew to Houston on Wednesday and was examined by back specialist Dr. Michael McCann, who administered the injection.
"Dr. McCann thought it went well, and there's still the potential of him starting on Sunday," Wade said. "There's a possibility we could have to push him back, but at this point everything has went well."
If Oswalt can't start Sunday, Wade said rookie right-hander Bud Norris would be in line to take his place. Norris made his Major League debut Wednesday and gave up one run in three innings.
Oswalt was on the DL in 2006 with a mid-back sprain and last year with a left hip abductor strain. An MRI of Oswalt's back taken last July showed a small disk protrusion.
Brian McTaggart is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.