According to local media, residents of Tonsberg, about 100 kilometres (60 miles) south of Oslo, noticed that the memorial had been defaced in the early morning of the anniversary of the attacks carried out by Neo-Nazi Anders Behring Breivik.
In 2011, Breivik, disguised as a police officer, tracked and gunned down 69 people, most of them teenagers, at a Labour Party youth camp on the island of Utoya, shortly after killing eight people in a bombing outside a government
building in Oslo.
The defaced memorial is part of a series of granite sculptures offered to the various municipalities where the victims were from.
Later on Monday police announced on Twitter that they had arrested two men, aged around 20, for vandalising the memorial.
"This is terrible. It's hard not to think that this is someone with a political motive," Norway's Prime Minister Erna Solberg told news agency NTB.
"If this is just a prank, it's extremely insensitive to do it on a day like this," she added.