Clarke was optioned to Triple-A Reno on Thursday.
The Diamondbacks need a fresh bullpen arm for Thursday's series opener against Atlanta after using eight relievers during Wednesday's extra-innings win over the Rays, so Clarke was shuttled back to the minors in exchange for Jon Duplantier. The right-hander held his own in his first career big-league start earlier in the week, allowing two runs on seven hits while striking out two in six innings. It remains to be seen whether Clarke will rejoin the big-league rotation later in the month. The Diamondbacks have yet to announce who will start in place of Clarke on Sunday, though Zack Godley is an option.