Police say the animal wandered through a gate that had apparently not been shut properly. It reached an adjacent storage building, where it attacked and killed the 43-year-old woman.
The tiger was then shot dead by the director of the zoo through a skylight, before it could get to public areas.
Members of the public were ushered to safety, and the zoo was briefly closed.
It is not the first time this year animals have escaped from their enclosures in a German Zoo.
Last month five chimpanzees broke out of their pen in Hanover. In that case, however, they were recaptured before anyone was hurt.
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