Marco Goecke was apparently furious about a review of one of his shows by journalist Wiebke Hüster.
He allegedly confronted Ms Hüster during the half-time break of another show and smeared a paper bag filled with dog excrement on her face.
Ms Hüster’s employer, the Frankfurter Allgemeine Zeitung (FAZ), said police were investigating.
The initial review of Mr Goecke’s show, In The Dutch Mountains, was described by Ms Hüster as like being “alternately driven mad and killed by boredom”.
Ms Hüster told the BBC she was in “shock” after what she described as a “brutal” attack.
Mr Goecke said he believed the damning review had cost the Hanover Opera House subscriptions and threatened to ban her from the opera house during the confrontation.
Hanover State Opera said Mr Goecke had been suspended with immediate effect, as his “impulsive reaction” went against its rules of conduct.
They said Mr Goecke “extremely unsettled the audience, the employees of the house and the general public and thus massively damaged the State Ballet”.
The statement also said that Ms Hüster’s “personal integrity was blatantly violated”.
The FAZ paper, for which Ms Hüster worked, described the incident as “an attempt to intimidate our free, critical view of the art”.