Mejia was optioned to Triple-A Rochester following Saturday's game, Mike Berardino of the St. Paul Pioneer Press reports.
The 23-year-old labored through 2.2 innings Saturday against Detroit, needing 70 pitches to record eight outs. It's uncertain who will replace Mejia in the rotation the next time the Twins need a fifth starter, but Jose Berrios is off to a strong start with Rochester, compiling a 1.42 ERA, 0.79 WHIP and 18:3 K:BB in his first 19 innings.