Wright was scheduled to start on Thursday. Manager Alex Cora announced Tuesday night that left-hander Brian Johnson will start Thursday's finale of the three-game series against the Los Angeles Angels.
Johnson is 1-2 with a 4.50 ERA in 36 innings. He last pitched Friday night against the Seattle Mariners, throwing 2 2/3 scoreless innings in a 14-10 victory.
Wright started that game and gave up 10 hits and 10 runs in 3⅓ innings, including three homers.
Wright, 33, is 2-1 with a 3.38 ERA in 10 appearances, including four starts, this season. He began the season on the 10-day disabled list recovering from left knee surgery and made his first appearance of the season May 15.
"I mean, it's frustrating because you want to go out there and compete," Wright told reporters Tuesday. "But when I had the surgery, they kind of told me this was going to happen -- you're going to have really good weeks, you're going to have really bad weeks and it's going to come to a point where you're not going to have to worry about it."
The move to the disabled list is retroactive to Saturday. The Red Sox called up right-handed pitcher Justin Haley from Triple-A Pawtucket to take Wright's spot on the roster.
Haley made his Red Sox debut June 13 at Camden Yards, pitching two scoreless innings in a 5-1 win over the Baltimore Orioles. He has a 3.06 ERA and 54 strikeouts in 12 starts for Pawtucket this season.