Burke was optioned to Double-A Frisco on Tuesday.
Burke spent 2018 at the High-A and Double-A levels of the Rays organization before coming over as part of the three-team Jurickson Profar trade in December. He'll return to the Double-A level, but if he can come anywhere close to the 1.95 ERA he posted in nine starts for Montgomery last season, he should earn a promotion soon.