CBS Sports' Jim Bowden reported the update Wednesday.
Smith has emerged as a crucial piece of the Astros' bullpen since being signed in December 2017. He compiled a 3.06 ERA and 0.99 WHIP with 68 strikeouts in 70.2 innings across 84 appearances over the past two seasons.
The 36-year-old Ohio native, who signed a two-year, $8 million contract extension with Houston during the offseason, owns a 2.98 career ERA in 13 years.
Astros manager Dusty Baker provided details about Smith's absence from camp in early July.
"Joe Smith has concerns about the health and safety of his family," Baker told reporters. "That is the reason for him not being in camp currently."
His absence will create a major void in the Houston bullpen.
Closer Roberto Osuna and set-up man Ryan Pressly will handle the final two innings in most close situations, but otherwise, the bridge between the club's rotation and that duo is uncertain. That's a bigger concern in the shortened season, especially with most starters' pitch count being limited at the outset.
Chris Devenski, Brad Peacock and Bryan Abreu lead the group of relievers likely to take on bigger roles in high-leverage situations. The Astros will likely be quick to change things up if any of them struggle, however, with far less wiggle room within a 60-game campaign.
Smith should return to his typical late-inning role if he returns to the Astros in 2021.
Bleacher Report's David Gardner interviews athletes and other sports figures for the podcast How to Survive Without Sports.