Police in Nyala, the capital of South Darfur state, fired tear gas at protesters throwing stones and burning tyres in the streets, witnesses said.
Several protesters chanted slogans calling for the government's downfall.
Since June, Sudan has seen sporadic protests against government austerity measures, including fuel subsidy cuts.
The country's authorities have been trying to cut spending since Sudan lost three-quarters of its oil revenue when South Sudan seceded last year.
Demonstrators in Nyala chanted "No to high prices" and "People want to change the regime", according to witnesses.
Bothina Mohmed Ahmed, a spokeswoman for the state of South Darfur, said it was not known how the six deaths had happened, and that an investigation had been launched.
Opposition activists and media accused the police of using live ammunition.
The protests started on Monday when local students "rejected the price of transport announced by the government", Ms Ahmed said, adding that "other groups" had joined the protests and attacked government buildings.
"This has been happening on the main roads and in the main market area. There's been some damage to buildings," African Union-UN peacekeeping mission spokesman Christopher Cycmanick told AFP.
The anti-austerity protests in Sudan began in June among students in Khartoum, but have since spread to other social groups and areas.
They had recently dwindled as a result of the Muslim holy month of Ramadan, which began on 20 July.
Until this year, Sudan had escaped the unrest characteristic of recent uprisings in Arab countries such as neighbouring Egypt, but correspondents say economic hardship caused by austerity has led to growing dissatisfaction with President Omar al-Bashir.
Six people have been killed in violent protests against high transport prices in the Darfur region of western Sudan, local officials say.