The warning came as a suicide bomber killed two pro-government fighters in a blast that targeted a checkpoint in the centre of Yemen's second city, a security official said.
Students said armed militants distributed leaflets containing the threats and signed by the Islamic State group in at least three departments of the university of Aden.
The leaflets also banned music and demanded that students perform collective prayers on campus, they added.
They set a Thursday deadline for the demands to be met.
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Otherwise they threatened to carry out car bomb and petrol bomb attacks.
The authenticity of the leaflets signed by the Aden and Abyan branch of IS could not be immediately verified.
Southern fighters allied with President Abedrabbo Mansour Hadi and supported by Saudi-led coalition forces managed in July to push Shiite rebels out of the port city of Aden.
But Islamist militants, including Al-Qaeda and the Islamic State group, appeared to have gained ground in the southern city, where jihadists are now visibly present.
On Monday, a man wearing an explosives belt detonated his bomb at checkpoint in the centre of Aden, killing two pro-government southern fighters and wounding a third, the security official said.
Al-Qaeda, active across several parts of Yemen, has exploited the collapse of central authority during a 2011 uprising that ousted veteran president Ali Abdullah Saleh.