The 28-year-old closer is in the midst of a remarkable season, posting a 1.08 ERA and 1.15 FIP over 25 innings this year while notching 11 saves. He's expected to garner trade interest as the deadline nears.
Giles was acquired last season from the Houston Astros in a deal involving Roberto Osuna.
Giles says he felt fine but that his recovery from back-to-back outings was a bit slower than normal, according to Shi Davidi of Sportsnet. He doesn't expect to stay on the IL longer than the requisite 10 days.
In a pair of corresponding moves, right-hander Clay Buchholz was removed from the 40-man roster and transferred to the 60-day IL, while right-handed pitching prospect Jordan Romano had his contract selected by the Jays.
Romano owns a 6.10 ERA and 1.36 WHIP in 17 games at Triple-A this year while working predominantly out of the bullpen.