The animals climbed out of their enclosures using sawed-off branches about 12:30 p.m. Wednesday, Bild reported.
One chimp knocked the 5-year-old to the ground, causing a head laceration and several bruises on her face, the newspaper reported.
Officials evacuated the zoo of its 2,482 visitors as zoo workers armed with stun guns and sharp weapons tracked down the animals. Police issued a command to shoot any chimpanzee that left zoo grounds, but after visiting the giraffe, an Alaska-Yukon Bay exhibit and the tropical house, four of the five chimps voluntarily returned to their enclosure.
The fifth chimp was lured back to the enclosure by a zoo worker and by 1:40 p.m. the gates of the zoo were reopened, Bild reported.