A photograph obtained by Fairfax of the speech, which was delivered at an event celebrating the 63-year reign of Queen Elizabeth II, revealed that it began with "I would like to start by acknowledging the traditional owner of this land: the Crown."
Linda Burney has responded by saying the remarks have "no place in modern Australia".
The Deputy Opposition Leader and spokeswoman on Aboriginal Affairs called out the comment on her Facebook page on Monday.
"The First Australians have been custodians of this land for over 40,000 years. Jokes like these have no place in modern Australia - and certainly not at a government sanctioned event,” she wrote.
The black-tie dinner was held in the private dining room of Don Harwin, the President of the NSW Legislative Council to raise funds for the Australia Youth Trust and was attended by NSW politicians.
Ms Burney told the Sydney Morning Herald: "Recognition and acknowledgment of country has become an important part of cultural protocol in Australia. Comments like these display appalling ignorance and crude insensitivity."
"Jokes like these have no place in modern Australia - and certainly not at a government sanctioned event"
Mr Harwin refused to reveal the identity of the speechmaker but claimed that the person was attempting to be "humorous". He added that it would have been better if the joke was left unsaid.
Conservative commentator Andrew Bolt later weighed into the mix by posting an excerpt of the original article on his Telegraph blog stating ‘If the Liberals apologise for this, too, I give up.’
He recently came under fire for saying that Adam Goodes should admit he was wrong for standing up to the racial slur by a thirteen year old in order to end the booing controversy that has haunted him during AFL games in 2015.
What is 'Acknowledgement of Country'?
Acknowledgement of country was first introduced to the opening of parliament in 2008. It is an official protocol that is conducted at many private and public events across the country.
In place of a Welcome to Country by an elder from the local community, an acknowledgement is conducted by the wider Australian society to recognise Indigenous Australians as the traditional owners of the land and acknowledge their contributions both past and present.
Though Acknowledgement of Country is not without its critics, 60 percent of surveyed Australians thought that Aboriginal ownership of the land should be acknowledged at welcoming ceremonies, as reported by Fairfax.