A Captain Cook statue, located at Cook's Cottage in Fitzroy Gardens in Melbourne, was destroyed in the early hours of Monday morning.
A group of four people were captured on CCTV sawing the bronze statue down, the City of Melbourne has said.
Victoria Police say they are investigating 'criminal activity' and assessing whether the statue can be repaired.
A video, posted by an anonymous account to Instagram, showed a person sawing the statue before it collapsed.
Alongside the video, the caption read, 'The colony keeps falling', with the group also claiming to have painted 'the colony will fall' on the ground next to the fallen memorial.
"Monuments such as this only serve to prop up the narrative that enables so-called Australia's continuing theft and desecration of land and life, and to legitimise its ongoing violence," the post reads.
"This narrative is as hollow as a monument to a long dead coloniser who met his just fate, being speared by First Nations warriors in Hawaii.
"The words 'the colony will fall' were painted beside the fallen statue – because we know the colony CAN, MUST, and WILL fall.
"The legacy of the imposter Australian empire is slowly but surely crumbling around us, piece by piece – brick by brick – statue by statue."
This is the third Captain Cook statue to be destroyed in Melbourne this year.
A statue in St Kilda was sawn off at the feet in a similar way prior to January 26 with the words 'the colony will fall' spray painted on the plinth where the monument once stood.
A second statue of Cook in Fitzroy was then found broken and covered in graffiti during the long weekend.
