The statue was found covered in paint on Thursday. Graffiti depicted an Aboriginal flag and the words: "We remember genocide".
Australia Day, the anniversary of British settlement, causes annual debate over indigenous sensitivities.
The Australian government said the vandalism was "disgraceful".
"These vandals are trashing our national heritage and should be prosecuted," tweeted Minister for Citizenship and Multicultural Affairs Alan Tudge.
He told local radio station 3AW: "I want Australia Day to be a great unifying day for our country. It has been for many decades now."
Police said they were investigating the incident but no suspects had been identified.
What has Australia Day caused controversy?
The national celebration falls on 26 January, the day in 1788 when Britain's First Fleet landed in Sydney Cove. Captain Cook had made it to Australia's east coast in 1770.
Many indigenous Australians have said Australia Day should be held on a different date, arguing the current celebration is hurtful.
Several protests are planned for around the nation on Friday after similar events in recent years.
However, the government has consistently defended the celebration.
Has this happened before?
Last year, a statue of Captain Cook in central Sydney was also vandalised with messages including "change the date" and "no pride in genocide".
It followed a high-profile public debate about whether it was appropriate for the statue to carry a plaque saying "discovered this territory".
Prime Minister Malcolm Turnbull condemned the vandalism at the time, drawing a comparison with Soviet dictator Joseph Stalin.
"When [Stalin] fell out with his henchmen he didn't just execute them, they were removed from all official photographs - they became non-persons, banished not just from life's mortal coil but from memory and history itself," he said.
"Tearing down or defacing statues of our colonial era explorers and governors is not much better than that."
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