Altuve said the injury felt better than he thought, but he added he wouldn't return until he felt ready.
"We're going to give this the time it needs," Altuve said Saturday. "I'd rather lose today or tomorrow's game than lose 20 games."
Marwin Gonzalez again replaced Altuve in Houston's lineup, batting ninth and playing second base.
"If he continued to make progress, it's better than being stagnant or feeling the same," Hinch said. "... The training reports are that he's continuing to take steps forward and feeling better. We'll continue to hope for that and get him in there as soon as we can."
• Hinch said Brad Peacock would arrive in Houston on Monday to be reevaluated after the right-hander left a rehab assignment at Double-A Corpus Christi on Thursday feeling "less than 100 percent."
Peacock, who has been on the disabled list since April 15 with a left intercostal strain, threw two scoreless innings in the start.
Chandler Rome is an associate reporter for MLB.com.
This story was not subject to the approval of Major League Baseball or its clubs.