Several government ministries, the German Intelligence Service, a courthouse and the Museum for Contemporary Art fall within the zone and were closed.
Police said they had no idea as yet how long the operation to defuse the bomb would take and would depend on the condition of the missile.
The police say there is no immediate danger from the 500 kg British bomb, which was found on Heidestrasse last Wednesday. But not generally this close to the city center, we're 300-400 meters from the main train station.
Buildings will be cleared in an 800m radius from the construction site where the bomb was discovered.
"For a bomber, this would have been a strategically important place", he said.
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Musk touched on why he was setting a higher target internally than the one the company has communicated publicly in his email. The automatic blog Jalopnik had first published Elon Musk's email on Tuesday and the authencity was confirmed by sources.
Police tweeted a photo of their bomb disposal team poised to make it safe.
Bomb disposal experts were able to successfully remove the detonator just after 1 p.m. and destroy it in a small controlled explosion.
DW reporter Rebecca Ritters was at the scene in Berlin and said the discovery of unexploded bombs was not uncommon in Germany with more than 2,000 tonnes of bombs and live ammunition unearthed across the country every year.
Flights from Berlin's Tegel airport are not affected but passengers have been warned that public transport to the city's two airports - Tegel and Schoenefeld - would be disrupted.
In one of the more sensational finds, a 250-kilogram (550-pound) British bomb was found in 2002 beneath the lower ring of seats during renovation work at Berlin's Olympic Stadium, where tens of thousands of fans regularly watch the city's Hertha BSC soccer club play its home games.