The tough new laws come under a plan to protect Australia's colonial history.
It will see statues over 100 hundred years old of the British navigator placed on the National Heritage List, which will provide the monuments with special protections under the heritage scheme's strict laws. It now means anyone who damages them could be fined or jailed for up to seven years.
The Federal Government has reportedly asked the Heritage Council to look at placing a number of Captain Cook statues on the register to discourage attacks on the historic monuments.
The new laws comes after a number of statues including that of Captain Cook were defaced in Sydney's Hyde Park.
Environment Minister Josh Frydenberg told Newscorp these actions should be condemned.
"When we saw those criminal acts on that Captain Cook statue, the Prime Minister was very quick off the blocks to condemn it and to remind everyone that we shouldn't be seeking to rewrite our history," he said.
Mr Frydenberg says the government is now seeking advice for further protections.
"We know that there are a number of monuments throughout the country, be they in New South Wales, Queensland, Victoria, celebrating Captain Cook's performance and contribution. They are more than 100 years old, and what I have done is I have sought the advice of David Kemp, the head of the Heritage Council, to protect these statues and monuments, whether it be on the heritage list or some other form of legislative protection, we are seeking his advice," he said.
As part of the plan, the government announced Kamay Botany Bay National Park in Sydney's south, home to Captain Cook's landing site, will be the 112th site on the National Heritage List.
It will be up to the National Heritage Council to evaluate the government's proposal and decide if the monuments should be placed on the register.
Liberal Senator James Patterson says the new scheme is a common sense move.
"They are part of our history, they are part of our heritage. We have laws to protect houses and other buildings of national significance. These are nationally significant monuments and institutions, and they should be protected as well," he said.
Mr Patterson says statues should be left as they are.
"We have Bill Shorten and going out saying he will put footnotes on every statue. If you want to rely on history, don't just rely on the monument, go out and read history, you will get a fuller picture of history. I think we should leave them as they are."
But Indigenous Labor MP Linda Burney told Sky News any significant colonial site needs context.
"The simple argument that I have been making, and many people have been making for some time, is that any significant colonial site obviously needs the context in which that site sits in. And there needs to be an Aboriginal perspective. And we are simply asking for truth telling," she said.
"Obviously we want to respect the whole story of Australia, but I do say the whole story of Australia."
Labor Senator Pat Dodson says while he doesn't condone defacing statues, the correct story should be told.
"The narrative of colonisation is being challenged, it has to be challenged. Because we have a diversity, but we also have a continuing injustice of how Aboriginal people were dispossessed of their lands and how they were treated. So that story has to be told and rectified," he told NITV News.
The Yawuru man, from Broome in Western Australia, suggests more statues of Indigenous heroes should be erected, like the great Dharuk leader, Fernando.
"[He] walked around the streets of London trying to bring attention to the genocide that was going on back at the turn of the century. There should be a statue of him right at the edge of Sydney, as far as I'm concerned," he said.
Mr Dodson says acknowledging and recognising Indigenous leaders will make a huge difference.
"The history enriches you. It's not one side or the other, its the enrichment of that history. It's a reopening and a reunderstanding of that history."