Altuve left Monday night's game at Detroit with a jaw injury after colliding with right fielder Jimmy Paredes while chasing a popup, but manager Bo Porter said the injury wasn't serious and Altuve was expected back in the lineup Tuesday.
Now he's left the team because of the death in the family, and Houston recalled infielder Jake Elmore from Triple-A Oklahoma City.
Porter said Altuve initially considered staying, but the manager insisted he go back to his native Venezuela.
"I said, 'No, you're going home. Because even if you were to stay here, your mind, your heart, your soul would be back there with your family, and at the end of the day, if you don't go, you actually probably will regret it,' " Porter said.
Porter expects Altuve to be back with the team -- and in the lineup -- on Saturday.
Players are allowed to stay on the bereavement list for a minimum of three days and a maximum of seven.
Altuve is hitting .333 with 51 hits and 18 RBIs.
Elmore was hitting .300 with 10 doubles, 15 RBIs and eight stolen bases for Oklahoma City.
Right-hander Bud Norris, who left Monday's game with lower-back spasms, says he's still experiencing some soreness, but he's hoping to throw a side session Friday.
"It's still pretty tight and sore. Just got to do treatment the next couple days and kind of go day by day," Norris said. "Possibly a side on Friday. We have an off day Thursday -- so it's a light side on Friday, and just kind of go from there."