Infielder Oswaldo Navarro was optioned to Round Rock to open a spot for Wright, who was 3-0 with a 4.93 ERA in nine starts at Triple-A.
Norris went 2-5 in nine starts with a 6.80 earned run average. He was examined in Houston on Friday and diagnosed with bursitis and biceps tendinitis.
Manager Brad Mills decided to let reliever Brian Moehler start in Norris' place Saturday against the Cincinnati Reds. Moehler started 29 games for the Astros last season, but has made all of his 12 appearances out of the bullpen. Mills doesn't expect him to last long on Saturday.
"Right now, we hope he might give us three innings and if he feels good, maybe send him back out for the fourth," Mills said. "He's not stretched out. We're going to need some help behind him."
Mills plans to see how things go Saturday, then decide on roles for his expanded bullpen. Chacin is in his second stint with the Astros, making four relief appearances earlier this month. Houston has three left-handers in the bullpen after the moves on Friday -- Chacin, Wright and Tim Byrdak.