The incident came after about 1 000 mourners had buried Ali Abaker Mussa Idris in a south Khartoum cemetery.
An AFP reporter said police resorted to tear gas as the angry crowd, shouting anti-government slogans, began moving out of the burial ground.
The public anger is the first major showing of discontent since dozens of people were gunned down in anti-regime protests last September.
Idris, a third-year economics student, died in hospital from gunshot wounds "after security forces used tear gas and opened fire with live ammunition" at the University of Khartoum demonstration on Tuesday, Amnesty International said.
In a statement on the interior ministry website, police did not say what killed the student.
Many of those who attended Idris's funeral were also students.
"Peace, freedom, justice!" they shouted before the tear gas sent them scattering into nearby streets in the neighbourhood near a major bus station in the capital.
"Revolution is the people's choice!" they called, after earlier shouting for the overthrow of President Omar al-Bashir's regime, which seized power in an Islamist-backed coup 25 years ago.
Idris was killed when about 300 students, many of them from Darfur, protested at the university on Tuesday.
Police said they had resorted to fired tear gas only when the rally tried to move out of the campus and into the surrounding streets.
Activists said dozens were also arrested.
The unrest on Tuesday and Wednesday was the most serious in Khartoum since thousands of people demonstrated after the government slashed fuel subsidies in September.
Amnesty International said security forces were believed to have killed more than 200 people at that time, many of whom were shot in the head or chest.
Authorities reported a toll of less than half that.
Sudanese have suffered nearly three years of rising prices since South Sudan separated in 2011 with most of united Sudan's oil production, which accounted for most of Khartoum's export earnings and half of its fiscal revenues.
Since late 2011, the Sudanese pound has lost about 50% of its value on the widely used black market, while hard currency is in short supply.
Inflation has been around 40%, and the deteriorating economy has contributed to unrest in Darfur.
In a report to be considered by the United Nations Security Council, UN chief Ban Ki-moon says the main cause of violence and displacement in Darfur is now resource-based clashes between communities, supported by tribal militias.
Over the past two years, Sudan's faltering economy has led to worsening crime and intercommunal clashes, Ban says, adding that some cash-poor paramilitaries have joined the tribal fighting over gold and other resources.
An 11-year-old rebellion also continues in Darfur, where about two million people are displaced, according to the United Nations.
Analysts say the government can no longer control its former Arab tribal allies, whom it armed against the rebellion.