Oh has a 2.68 ERA in 47 innings this season, striking out 55 batters. The right-hander has been stellar this month, holding opponents to a .143 batting average.
Oh previously spent two seasons with the St. Louis Cardinals after several professional seasons in Japan and his native South Korea.
Toronto signed him to a one-year deal with a club option for 2019 this past offseason.
In return, the Blue Jays received minor league infielder Chad Spanberger, outfielder Forrest Wall and a player to be named from the Rockies.
The Associated Press contributed to this report.