Repair workers had discovered that the “big parts” of the plates covering the roofs were missing on Friday, said Berlin police.
Local newspaper B.Z. said the damage reached several hundred thousand euros and that three of the four entrance buildings were hit.
The Victory Column standing in central Berlin is one of the capital’s most recognisable landmarks.
It originally stood in front of the Reichstag parliament building, before being relocated by the Nazis in 1938 to its current location at a key roundabout at Tiergarten park.
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Germany’s monuments and museums have been hit by several high-profile thefts.
In 2017, burglars made away with a 100-kilogramme (220-pound), 24-karat giant gold coin from Berlin’s Bode Museum.
Two years later, thieves broke into a state museum in Dresden, snatching numerous pieces of priceless 18th century jewellery.