Giles was expected to be a major part of Seattle's bullpen after missing all last season following Tommy John surgery.
Giles had 23 saves and a 1.87 ERA in 53 appearances with Toronto in 2019. He pitched in just four games during the pandemic-shortened 2020 season before realizing he needed elbow surgery.
"Just gotta be patient. And trust me, I've done a lot of waiting and patience for the last over 500 days. So I think I can deal with a little bit longer," Giles said.
Giles' setback is the second injury in Seattle's bullpen. Seattle lost reliever Casey Sadler for the season because he needs shoulder surgery, but the team moved quickly to replace him by signing veteran Sergio Romo to a one-year deal.
Manager Scott Servais also said 2020 American League Rookie of the Year Kyle Lewis could start taking on a designated hitter role in minor league spring training games as he recovers from knee issues that limited him last season.