The British-made bomb, which weighs 1.8 tonnes and is two metres in length, was found during building work on the Wismarer Strasse in the Westend district, according to the Frankfurter Rundschau. German media said the bomb was nicknamed "Wohnblockknacker" (blockbuster) during the war for its ability to wipe out whole streets or buildings.
A police spokesperson said on Wednesday that 70,000 people will likely have to leave their homes, meaning that almost one in ten of the city's 717,000 inhabitants will be affected.
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Officers are guarding the site and there "is currently no danger".
Police said the bomb in question was a HC 4000, a so-called high capacity bomb used in air raids by British forces.
"Due to the large size of the bomb, extensive evacuation measures must be taken," police said.
The Wismarer street where the ordnance was found is close to the city centre and just some 2.5 kilometres north of the main Zeil shopping area. Among the affected buildings are the German Federal Bank and two hospitals.
Police expect Sunday’s evacuation to be completed by midday so that they can get on with disposing of the bomb.