Keepers were quickly alerted to the incident and rushed into the enclosure to get the bear away from the woman.
A police spokesman said the woman, who is thought to be mentally disturbed, was bitten in the arms and legs before zoo staff could push the bear away.
The animals were being fed at the time the woman jumped into their enclosure, at around 10:30 am.
Zoo biologist Heiner Klös said, “Our alarm system worked, otherwise it would have been a bad outcome for the bear as well.”
A zoo spokesman said the animal concerned was not Knut, the polar bear which became of global interest after being hand-reared.
The woman was treated at the scene for bite wounds and then taken to hospital.