Sobotka was outrighted to Triple-A Nashville on Wednesday.
Sobotka (illness) has appeared in two games for Triple-A Nashville so far in June, working scoreless innings Thursday and Sunday.
Sobotka has yet to pitch for Triple-A Nashville this season due to a sinus infection, Tom Haudricourt of the Milwaukee Journal Sentinel reports.
Sobotka was traded from Atlanta to Milwaukee along with Patrick Weigel on Tuesday, with Orlando Arcia going the other way.
Sobotka was optioned to team's alternate training site Sunday.
Sobotka was recalled by Atlanta on Saturday.
The Braves optioned Sobotka to their alternate training site in Gwinnett on Monday.
Sobotka was recalled from the Braves' alternate training site Saturday.
Sobotka was returned to the Braves' alternate training site Sunday.
The Braves recalled Sobotka from their alternate training site ahead of Sunday's doubleheader with the Phillies.