A police patrol noticed the man lying on his back with the majority of his body burned at the Place des Nations at around 1.10am.
At his side was a melted jerrycan that had contained petrol, police said in a statement.
Nearby a poster with a photo of a Tamil Tiger soldier and documents concerning various cases of immolation that took place in Tibet, the statement said.
Emergency officials rushed the man to the Geneva university hospital.
He was subsequently transported by helicopter to the burns treatment centre at the Lausanne university hospital (CHUV), where he died in the late afternoon, police said.
Police were unable to immediately identify the victim.
It is not clear whether he was an expat Tamil.
However, Tamils regularly demonstrate outside the UN offices and those of the Geneva-based UN Human Rights Council over issues related to Sri Lanka, a country torn by a 26-year-long civil war that ended in 2009.
An estimated 800,000 Tamils were driven from Sri Lanka to escape the civil war, with around 50,000 refugees ending up in Switzerland.