Nastrini was optioned to Triple-A Charlotte on Sunday.
Nastrini has struggled in his six starts in the majors this season, posting an 0-5 record with an 8.39 ERA, 1.99 WHIP and 19:25 K:BB over 24.2 innings. The White Sox called up lefty reliever Sammy Peralta from Charlotte in a corresponding move, but it's not immediately clear whom the big club may turn to as a replacement in the rotation for Nastrini.