Local authorities have advised residents to stay indoors and call the police if they saw any of the animals.
It was not immediately clear how the zoo animals escaped, but German media reported that they may have broken out after flooding from an overnight storm.
It is unclear what circumstances lead to the bear's death.
Those living nearby have also been asked to report any sightings of the big cats, now loose in Western Germany.
The animals included two lions, two tigers, a bear and a jaguar, according to several news reports.
According to the German broadcaster, heavy rain meant the water level increased and nearly the "entire zoo was flooded".
FBI Warns About Hackers Infecting Routers to Collect Information
The security experts added that the most vulnerable devices were manufactured by Linksys, Mikrotik, Netgear, QNAP and TP-Link. Talos, the threat intelligence agency for Cisco, estimated that 500,000 devices in 54 countries have been infected.
'Murdered' Russian journalist Arkady Babchenko is alive
Mr Babchenko, a high-profile critic of the Kremlin, appeared at a press conference on Ukrainian TV on Wednesday. Babchenko fled Russian Federation in 2017 after stating that he was receiving death threats over his reporting .
Zarif, Sushma to meet for talks on Monday
As for Saarc minus Pakistan , she said the South Asian bloc would not remain a grouping if a country went out. India imported $10.5 billion worth of goods, mainly crude oil , and exported commodities worth $2.4 billion.
The Eifel zoo, owned by the Wallpott family, is home to around 400 animals, also including a Siberian tiger.
Most were found on the grounds of the zoo and returned to their cages.
A bear has been shot just outside of its enclosure, say a spokesman for the zoo.
Animal escapes from zoos are rare but not entirely unheard of.
In an earlier zoo incident two year ago, two lions broke out of their cages at the Leipzig zoo.
In the end, a drone sighted the remaining escapees inside the zoo compound.