Smith, who is in his third season with the Astros, has not reported to summer camp because of a family matter, manager Dusty Baker said.
It remains unclear whether he will play in the shortened 60-game season.
Smith's mother is battling Huntington's disease, which has no cure, and the pitcher has been public about her condition.
Smith contributed to the Astros' 2019 postseason run with a 3.12 ERA in 10 appearances, eight of which were scoreless.
He recovered from surgery on his left Achilles last season and struck out 22 over 25 innings over 28 appearances, posting a 1.80 ERA.
The Astros re-signed him in December to a two-year deal for $8 million.