The unrest yesterday was the most serious in Khartoum since last September, when thousands of people took to the streets after the government slashed fuel subsidies.
In a statement on the Interior Ministry website, police did not say what killed the student at the University of Khartoum.
Police "got information that two students were injured and taken to hospital. One of them died," said the statement.
It added that police had already pulled back after earlier firing tear gas when the demonstrators tried to move their rally off campus.
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Students retaliated by throwing stones at the officers.
"Peace, peace for Darfur!" they called, adding: "We want to bring the criminals to the ICC!"
One student, who asked not to be named, said one of his colleagues had been wounded in the leg and taken to hospital.
President Omar al-Bashir and his Defence Minister Abdelrahim Mohammed Hussein are both wanted by the Hague-based International Criminal Court (ICC) for alleged war crimes in Darfur.
During last September's protests demonstrators called for the downfall of the regime, and Amnesty International said security forces were believed to have killed more than 200 people, many of them shot in the head or chest.