The team made the announcement about 90 minutes after Tuesday's non-waiver trade deadline.
Sale has been arguably the best starter in the majors this season, with an AL-best 2.04 ERA and an MLB-best 207 strikeouts in 141 innings. He is 5-0 in his last six starts, striking out at least nine in each, and hasn't given up a run in his last three outings.
Red Sox president of baseball operations Dave Dombrowski said he believes Sale's absence will be "more of a short-term type thing."
"He just said it's really been more mounting. It's been something that's bothered him a little bit," Dombrowski said.
"We really don't want to take any chances with it."
Boston leads New York by five games in the AL East. The move is retroactive to Saturday, meaning Sale could start again on Aug. 7, when Boston plays the Toronto Blue Jays.
"If we were in a different position and they needed me to make this next start, I would be out there pitching,'' Sale said. "I would make that start in two days.''
This will be Sale's first stint on the DL since 2015, when he was out to start the season with a fractured right foot sustained when he landed awkwardly getting out of his truck.
"I don't like this," the AL All-Star starter said. "I'm a pitcher who pitches."
In a corresponding roster move, the Red Sox recalled reliever Brandon Workman from Triple-A Pawtucket.
While the Red Sox hope to get Sale back soon, they don't expect second baseman Dustin Pedroia to return this season, Dombrowski indicated Tuesday.
"Maybe he will come back in September but there are no assurances to that," Dombrowski said, according to The Boston Herald.
Dombrowski has previously said it's likely the 34-year-old Pedroia won't be back until very late in the season, if at all, and he reiterated that Tuesday, underscoring that the team is guarding against rushing him back.
"I can't say I don't expect it but we're not anticipating it," Dombrowski said, according to WFXT-TV. "We called him last night so he wasn't caught off guard. He doesn't need pressure to return. If he does [return], we will happily deal with it when it happens."
Pedroia has played just three games this year after cartilage-restoration surgery on his left knee in the offseason.
Dombrowski said Monday that he expects newly acquired Ian Kinsler to be the regular second baseman, moving Brock Holt and Eduardo Nunez back into utility roles once third baseman Rafael Devers (hamstring) comes off the disabled list.
"Ian's a really good defensive player,'' Dombrowski said. "Basically, it's what we hoped, early this season, that Dustin would be.''