The culprits got away with the contents of more than 100 safe-deposit boxes from the branch in the south-west district of Mariendorf, a police spokesman said.
The bank's ATMs were damaged but not robbed. Nobody was hurt in the explosion.
Police don't know exactly what was stolen as safe-deposit box owners don't have to report their contents to the bank.
“The robbers must have had insider knowledge,” one policeman told the Berliner Morgenpost, noting that they knew about the location of the cellar containing the safe-deposit boxes as well as the building's security system.
After breaking in through a side exit to the branch, the robbers did serious damage to the building with the bomb, which went off at around 6.50 am.
Large window panes were dislodged from their frames and splinters flew across the Mariendorfer Damm road.
Eyewitnesses said that they saw a dark-coloured getaway car fleeing the scene shortly afterwards.
Firefighters rushed to the branch and were able to bring the fires left by the blast under control within an hour.
Experts said that there was no structural damage to the building, and tenants were able to return to their homes later in the morning.
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