Dave Dombrowski, Red Sox president of baseball operations, told reporters Smith suffered a subluxation of his right shoulder after throwing his glove in the dugout during Monday's 6-5 loss against the Oakland Athletics.
"It's got the potential of being a major injury," Dombrowski said.
Dombrowski noted Smith is seeking a second opinion on the injury, and the team hasn't put a timetable on his return.
The Red Sox announced Smith has been placed on the 10-day disabled list. Left-hander Bobby Poyner was recalled from Triple-A Pawtucket to take his spot on the 25-man roster.
Smith allowed a home run to Khris Davis in the eighth inning on Monday that gave the A's a 6-4 lead.
Boston acquired Smith from the Seattle Mariners in December 2015. The 28-year-old appeared in just three games during the 2016 season before undergoing Tommy John surgery.
Smith returned to the Red Sox's bullpen last September and appeared in eight games during the regular season. He also pitched 1.1 scoreless innings over two games in the ALDS against the Houston Astros.
The right-hander has a 3.77 ERA with 18 strikeouts in 14.1 innings this year. Smith's 18 appearances this season are tied for most on Boston's pitching staff.