Merryweather has made 26 appearances with the Blue Jays this season registering a 6.75 ERA and 1.43 WHIP.
The 30-year-old reliever faced seven batters during the eighth inning of Tuesday's wild 18-11 victory over Philadelphia and gave up five runs, all earned, on three hits with two walks and one strikeout.
Griffin will be active for Wednesday night's game on the road against the Philadelphia Phillies.
The 27-year-old has pitched 4.1 innings over five games with the Kansas City Royals this season with a 12.46 ERA and 2.31 WHIP. He was traded to the Blue Jays on July 16 for right-hander Jonatan Bernal.
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