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.

Millie the cat has been left with a suspected broken jaw from the attack, which the RSPCA described as "sickening".
The video shows two men walking towards Millie in Derby, then one kicks her and she flies several feet in the air.
It happened outside the Guinness Trust flats in Sidney Street at about 16:25 GMT on Thursday.
RSPCA inspector Sarah Burrows said: "It is an unprovoked attack which has sadly left Millie with a suspected broken jaw.
"Inflicting such a horrific attack on a defenceless cat is sickening and it's important we track down the people responsible."
The charity asked anyone with information to contact them.
They warned that anyone found guilty of causing unnecessary suffering to an animal could face up to six months in prison and a fine of up to Â£20,000.

Holyrood backed a series of opposition amendments following a Scottish government debate on patient safety.
They included a Lib Dem mention of a "recruitment crisis" and Labour warnings that services are "near breaking point".
This left the SNP voting against Shona Robison's amended motion, but they were defeated by opposition members.
Health Secretary Ms Robison had put forward a motion highlighting the work of the government's "world-leading" patient safety programme.
It said the programme "represents the international benchmark for safe care" and noted "the huge challenges that face the NHS in meeting the demands of an ageing population and those of integrating health and social care services".
Members unanimously backed a Conservative amendment from Donald Cameron adding that the health service is "facing severe workforce and staffing issues", and that "further action on staffing must be a priority".
Another amendment from Labour's Anas Sarwar was then passed by 62 votes to 61, adding in claims that "services are facing a situation in which demand is often outstripping supply". It also cited a report from the British Medical Association that the NHS is "near breaking point".
A further amendment from Lib Dem Alex Cole-Hamilton highlighted a "recruitment crisis" in the NHS, raising fears it could "pose a risk to patient safety", and was passed by the same margin.
The amended motion was then passed by 62 votes to 61, with SNP members voting against.
Six people have been killed in violent protests against high transport prices in the Darfur region of western Sudan, local officials say.
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The RSPCA is trying to find a man who was caught on CCTV kicking a cat "very hard" into the air.
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MSPs have passed a motion warning that patient safety is at risk amid a "recruitment crisis" in the NHS.