The German block was built in the 1960s and houses at least 72 people.
The type of cladding used at Grenfell Tower was reportedly banned in Germany.
Since the 1980s only non-flammable material can be used on the external walls of buildings greater than 22m in height.
Police cordoned off the building in the Hilgershöhe district of Wuppertal on Tuesday afternoon and buses were made available to move residents to alternative accommodation.
"There is danger in delaying, so we have to deal with it immediately," Martina Eckermann told Der Westen website.
The residents were told they should be able to return to their homes as soon as the cladding had been removed.
Since the 14 June Grenfell Tower fire, authorities have begun inspecting flats across England and found that cladding on 95 high-rise buildings is unsafe.
At the weekend, hundreds of flats were evacuated from the Camden area of north London because of safety concerns over cladding and other fire risks.
During the last fire inspection of the Wuppertal block, flammable insulation material was found with a wooden sublayer, and concerns were raised about narrow corridors and a lack of fire alarms, the head of the city's building department was quoted as saying. Escape routes could quickly become filled with smoke in the event of a fire.
Flats evacuated over fire risk fears
Residents were told to take only one suitcase before the building was sealed to prevent looting. They were due to be moved to flats that had been intended for refugees but were now empty.
Testing is expected to take place on another 70 buildings in Wuppertal.
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