Gregerson left the team before Wednesday night's game in Texas after his wife went into labor in Orlando, Florida. She gave birth to a baby boy.
Manager A.J. Hinch was unsure how long Gregerson would be out.
Hinch said the Astros are supportive of Gregerson, and that the team will figure out the bullpen while he's gone.
Gregerson has 27 saves, the most for an Astro since Jose Valverde had 44 in 2008. Gregerson last pitched Sunday, with a perfect inning for a save in the series finale at the Los Angeles Angels, which was his first appearance in a week.