The incident occurred when zookeepers were feeding the animals, one of whom attacked the intruder. She received bites to her arms and legs, but staff managed to repel the bear, the BB station said.
The woman was taken to Virchow hospital in Berlin.
The cause of the incident is being investigated. Police suspect the woman is mentally ill as she "did not fall into the cage accidentally but jumped there herself."
Last December, a man who later described himself as "lonely" jumped into the cage of the zoo's most famous polar bear, but emerged unscathed after zookeepers managed to distract Knut with beef.
The radio said the celebrity bear, who won the sympathy of millions of people from all over the world because he was abandoned by his mother shortly after his birth, was not involved in Friday's incident as he lives in a separate cage.
A spokesman for the zoo said Knut, now two years and four months old, would never harm a human.
