Jackson was optioned to Triple-A Oklahoma City on Tuesday, Juan Toribio of MLB.com reports.
He provided some short-term bullpen depth while Tyler Anderson was on the paternity list, but Jackson will head back to Triple-A for now. The 26-year-old righty logged a 5.00 ERA, 1.70 WHIP and 76 strikeouts in 75.2 innings at Triple-A and has only made two appearances in the majors this season.