A statue of Captain James Cook and a memorial to explorers Burke and Wills have been vandalised in Melbourne in the lead up to Australia Day.

Pink paint was dumped on Capt Cook's head at St Kilda on Thursday, with the words "no pride" painted beneath his feet, along with the Aboriginal flag.

A bluestone monument near Melbourne Zoo marking Burke and Wills' journey to Australia's interior has also been vandalised, with green paint and the word "stolen" daubed on it.

AAP

Federal citizenship minister Alan Tudge said the vandalism is a "disgrace".

"These people are trashing our national heritage by doing what they're doing and they're achieving nothing in the process," he told 3AW radio on Thursday.

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"You can't rewrite our history.

"I want Australia Day to be a great unifying day for our country, it has been for many decades now."

Australia Day has been marked by a public holiday on January 26 since 1994, to mark the arrival of the First Fleet in Sydney, but had been recognised on numerous other dates in previous decades.

Victoria Police is investigating the vandalism.