In addition, wild animals have broken out of the zoo.
Local authorities advised residents to stay inside their homes and call police if they see anything.
The animals are said to have escaped when when a storm hit the area and caused floods.
It is unclear what circumstances lead to the bear's death. A massive hunt is under way for the five big cats.
Vets are said to be on sight as well as police and firefighters.
Large predators are among the main attractions at the zoo, which is home to about 60 different species, including Siberian tigers and African lions, on about 30 hectares of land.
A spokesman for the district of Bitburg-Pruem, in the state of Rhineland-Palatinate, said earlier in the day that two lions, two tigers and a jaguar were on the loose. At the zoo, which is located on a riverbank, the water was knee-high. An escaped bear was found and had to be shot dead.
This escape has come two years after another similar case happened in eastern Germany, when two lions broke out of their cages at the Leipzig Zoo, in Leipzig, the AFP reported.
The 74-acre zoo offers many attractions including a cable auto and a miniature village.
In the end, a drone sighted the remaining escapees inside the zoo compound.