The Governator, being Austrian-born, is fluent in German.
However, when his movies are dubbed into German, he doesn't provide his own voice. He is dubbed by a German voice actor instead, because Arnie's Austrian accent is too thick. (To a speaker of standard High German, the southern dialects like Bavarian and Austrian sound quaint and "mountain rural" at best, incomprehensible at worst.)
The voice actor who dubs Arnie is also the regular German voice for Sylvester Stallone and John Travolta, which would cause an interesting dilemma if they all ever decided to sign up for the same movie.