Smith was available for Tuesday night's game against the Chicago White Sox, giving Boston another bullpen option in the seventh and eighth innings.
Smith strained a flexor muscle in his right forearm in a spring training game. He retired all five batters in two rehab relief appearances for Double-A Portland last week.
The Red Sox optioned infielder Marco Hernandez to Triple-A Pawtucket on Sunday night in anticipation of the move.
The 26-year-old Smith was acquired from Seattle in the Wade Miley trade in December after posting a 2.31 ERA in 70 appearances as a rookie with the Mariners in 2015.