Lucas Harrell will get the start in Norris' place.
The 28-year-old Norris, who was selected by the Astros in the sixth round of the 2006 First-Year Player Draft, continues to be the subject of trade rumors as the deadline approaches.
According to Yahoo! Sports Jeff Passan, it's very likely the Astros will trade Norris at some point today.
Houston appears motivated to move Norris, with Passan noting the Pittsburgh Pirates as a potential landing spot.
MLB.com's Brian McTaggart reports that three teams are pursuing Norris.
Norris has posted a 6-9 record with a 3.93 ERA and 90 strikeouts over 126 innings in 21 starts with the Astros this season.
He isn't eligible for free agency until after the 2015 season.