They remained on the building's roof for 10 minutes before security asked them to leave.
The student group Fossil Free MU launched the fossil fuel divestment campaign in June 2013.
The nude students held a banner that read: 'No sustainability without divestment' on the roof of the Old Quad
In three years of campaigning, the students have held referendums, rallies, and forums to engage students, staff and the university council to promote divestment.
Since late 2015, the group have been engaging with the University's Sustainability Executive to push for divestment via formal pathways.
But in a meeting conducted last Thursday between Fossil Free MU members and Chief Financial Officer Alan Tait, Mr Tait reiterated the university's stance that they would not be committing to divestment.
'Rapid divestment from fossil fuels is a crucial step on the pathway to a safe climate future,' said Professor John Wiseman, Deputy Director of the Melbourne Sustainable Society Institute.
The group is protesting against the university's administration after it was revealed that it would continue to invest in the fossil fuel industry.
'Divestment from fossil fuels is therefore an urgent ethical and financial responsibility for all Australian investors and institutions – including universities.'
The current campaign is part of a national fossil fuel divestment effort that is taking place at seven universities across the country, including the Australian National University, The University of New South Wales, the University of Queensland, the Queensland University of Technology, The University of Sydney, and Monash University.
Two universities, the University of Sydney and the Australian National University, have already made partial divestment commitments, and Swinburne University is in the process of seeking an investment fund that can provide a fossil free portfolio.
The student group Fossil Free MU launched the fossil fuel divestment campaign in June 2013 at the University of Melbourne (pictured) - Since the publication of this article, the University's Senior Media Advisor, David Scott, insists that a final decision on divestment is yet to be reached, as the University is still in the midst of a public consultation process, around both the sustainability charter and sustainability plan.