KARLSRUHE, Germany — Pushing a stroller toward the rehearsal space of the Badisches State Theater in Karlsruhe, a pleasant city in southwest Germany, Anna Bergmann stopped to comfort her 2½-year-old son, whose sunny demeanor had suddenly dissolved into heart-rending sobs. Luckily, the prospect of a chase around the fountain soon cheered him up again. “It really puts rehearsal terror in perspective,” said Ms. Bergmann, the theater’s new playhouse director, shaking her head.

Ms. Bergmann is the first woman to hold that position, overseeing theater at the large, state-funded institution that also stages opera, ballet and other performing arts.

Despite her being well known in German theater circles, her appointment was something of a statement in an overwhelmingly male-dominated field. Her first major decision, however, was downright radical: Tired of hearing that theaters would like to hire female directors but could find few, she said she wanted women to lead most of the productions during her first season at the helm. The State Theater’s general director, Peter Spuhler, who oversees the institution as a whole, proposed going further: Why not exclusively use female directors, for once?