The family home of James Cook, which was transported from England for display in Melbourne's Fitzroy Gardens in 1934, has been spray-painted with graffiti, including "26th Jan Australia's shame" and "F*** Aus Day".
The British explorer is credited with the first recorded European discovery of Australia's east coast.
Dr Calma says it is not acceptable for people to vandalise a heritage site.
"We don't know who did that painting, whether it was an Indigenous person, whether it was a non-Indigenous person, whether it was a kid, whether it was an organised group," he told SBS. "It is not acceptable and we should all take pride in Australia as a great nation".
The building was vandalised with similar slogans in February last year.
Anarchist blog "disaccords" claimed responsibility for the 2013 graffiti, saying in an online statement the denial of Australia's "brutal" history was nowhere more evident than on Australia Day.
Melbourne Lord Mayor promises more security
Smashed light bulbs were used as makeshift paint bombs, breaking one window and littering the building's surroundings with glass.
Melbourne Lord Mayor Robert Doyle said CCTV cameras, added after last year's attacks, had caught footage of the vandals and more security had been added to the cottage.
"We'll put security on there from now until early next week so it'll be under guard," Mr Doyle said.
"We were actually planning on doing that for this weekend but unfortunately these vandals got in in advance."
Victoria Police say at least two vandals had been spotted on camera during 2.30am and 2.40am.
Senior Constable Scott Gray said the people responsible knew where security cameras were in the park, and how to avoid them.
"They seem to know where the cameras are placed around the gardens," Det Snr Const Gray said on Friday.
A damage bill for the graffiti and broken window has not been finalised but the cottage, which attracts 100,000 visitors a year, will be reopened on Friday afternoon.
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