Manager Dusty Baker said Valdez sustained the cut after putting his hand on the outfield wall during batting practice at the year-old home of the Rangers.
Baker said the club still hoped he could make the start against Rangers rookie Glenn Otto in the finale of a four-game series. Instead, it will be a matchup of rookies with right-hander Luis Garcia making his 26th start for the Astros.
Houston has openings in the rotation Friday and Sunday for a weekend series at home against Arizona, and Valdez could fill one of those spots. Righty Lance McCullers is set for Saturday.
Valdez cut the same finger that he broke early in spring training when he was hit on the hand by a line drive from Francisco Lindor of the New York Mets. The 27-year-old missed the first two months. Valdez is 10-5 with a 3.26 ERA in 19 starts.