Per Bob Dutton of the Tacoma News Tribune, Smyly is expected to miss six to eight weeks due to a flexor strain in his left elbow.
Smyly originally suffered the injury on Tuesday during a between-start bullpen session, per Dutton.
The Mariners acquired Smyly from the Tampa Bay Rays during the offseason. The 27-year-old tossed a career-high 175.1 innings last season, though he also posted a career-worst 4.88 ERA with 32 home runs allowed.
Smyly was penciled in as part of a Seattle rotation that also includes Felix Hernandez, Hisashi Iwakuma, James Paxton and Yovani Gallardo. Dillon Overton could be bumped into the rotation to take Smyly's spot for the time being.