Over his three-year career with Toronto, Jenkins owns a 3.82 ERA and has appeared in 26 games.
In 13 games with Buffalo this year, Jenkins has posted a 1-3 record with two saves and a 4.01 ERA.
Toronto optioned starting pitcher Liam Hendriks to Triple-A following Sunday's 4-0 win over the Royals to account for the corresponding roster move.
Gregor Chisholm is a reporter for MLB.com. Read his blog, North of the Border, and follow him on Twitter @gregorMLB. Joey Nowak is a reporter for MLB.com. Follow him on Twitter at @joeynowak. This story was not subject to the approval of Major League Baseball or its clubs.