The statue, which has already been cleaned, was found today covered in bright pink paint, graffiti depicting an Aboriginal flag and the words “We remember genocide”.
The Australian government said this act of vandalism was “disgraceful”.
Alan Tudge, Minister for Citizenship and Multicultural Affairs, tweeted: “These vandals are trashing our national heritage and should be prosecuted.”
The national celebration falls on the anniversary of British settlement, 26 January 1788.
Captain Cook is part of the country’s history as he reached Australia’s east coast in 1770.
Many indigenous Australians deem celebrating these two events hurtful and have asked to move Australia Day to another date.
Several protests are planned around the country on Friday.
However, the Australian government defends the celebration.
Mr Turge told to radio station 3AW: “I want Australia Day to be a great unifying day for our country.
“It has been for many decades now.”
Police are investigating the incident but so far no suspects had been identified.
Another statue of Captain Cook in central Sydney was vandalised last year.
Messages written on it read “change the date” and “no pride in genocide”.
The act was condemned by Prime Minister Malcolm Turnbull, who drew a comparison with Soviet dictator Joseph Stalin.