Prior to Sunday's 5-4 loss to the Blue Jays, he was placed on the 15-day disabled list.
"He's going to be immobilized for two weeks, and we'll re-evaluate at that point to see what the next steps are," Red Sox manager John Farrell said. "He sustained a pretty severe ankle sprain here yesterday."
The Red Sox also placed catcher Ryan Hanigan on the 15-day disabled list with a neck strain.
"He had the MRI performed this morning," Farrell said. "He's got some inflammation in the neck, the strain that's there. He's going to remain back here and continue to receive treatment rather than go to the West Coast."
The injury to Swihart was untimely, given the nice adjustment he made to left field and the fact he had been swinging the bat better of late. Swihart also could have filled in for Hanigan at backup catcher during his absence.
Instead, Boston had to purchase the contract of catcher Sandy Leon from Triple-A Pawtucket and recall outfielder Rusney Castillo.
Boston also swapped out righty relievers, with Heath Hembree getting recalled from Pawtucket while Noe Ramirez was optioned to Triple-A. Hembree pitched 2 1/3 innings of hitless, scoreless relief Sunday, striking out four.
Swihart had come back from Triple-A to replace Brock Holt, who has been out since May 19 with a concussion.
"Yeah, the injuries are unfortunate, taking both guys out, but we feel confident with Sandy Leon and the number of games caught here last year," Farrell said. "We're hopeful that the progress that Brock Holt has made here of late continues and he's out on a rehab assignment hopefully by the time we get to Minnesota. That would be optimistic. We'll miss the additional left-handed bat. We're trying to find ways to supplement that right now."
Castillo, who has had a hard time generating any momentum since signing a seven-year, $72.5 million contract in August 2014, will be used as a backup during his stint with Boston. Chris Young, who had a homer and a single on Sunday, will be the starting left fielder until either Holt or Swihart returns.
"We'll try to see if there's some spots where he ends up in the starting role," Farrell said of Castillo. "The fact that he can play all three outfield positions defensively is certainly an asset in this case. Chris Young will be the starter in left field for the foreseeable future."
For Castillo, 28, this will be his third Major League stint in 2016. He is 2-for-4 with a double in two games for Boston this season. Hembree, 27, returns to the Red Sox for his second stint in the Majors this season. He is 2-0 with a 2.14 ERA and 18 strikeouts in 12 appearances.
This will mark the first Major League time the 27-year-old Leon will see this season. He was hitting .243 with three doubles and two home runs in 36 games for Pawtucket.
Ramirez, 26, has a 6.55 ERA in 11 appearances over five different stints with the Sox this season.