Bread prices more than doubled last week as flour manufacturers raised prices on dwindling wheat supplies after the government decided to stop importing grain and allowed private companies to do so.
Sporadic anti-government protests have been held since Saturday in some parts of the country following the price rise.
They were staged again on Monday in the area around Khartoum University, triggering clashes between students and anti-riot police.
"No, no to high food prices," students shouted as they attempted to leave the university campus but were quickly pushed back by dozens of anti-riot police who fired tear gas at them, the AFP correspondent reported.
The protesters then threw stones at the police who closed the main road to the university as thick plume of black smoke billowed over the campus.
Dozens of police in plain clothes were deployed around the university, as the authorities warned of a crackdown.
"Police will crush any protest that results in destruction of property," Minister of State for the Interior Babikir Digna said, according to the official SUNA news agency.
In another protest at Kosti in the state of White Nile, several school children staged a demonstration but it was swiftly broken up by baton-carrying police, witnesses said.
On Sunday, a student was killed during protests in the town of Geneina in war-torn Darfur. It was still unclear how he was killed.
Leading opposition groups have called for anti-government protests after the cost of flour jumped to 450 Sudanese pounds ($25) for a 50-kilo (110-pound) sack from 167 pounds.
Similar protests were held in late 2016 after the government cut fuel subsidies.
The authorities had cracked down on those protests to prevent a repeat of deadly unrest that followed an earlier round of subsidy cuts in 2013.
Dozens of people were killed in 2013 when security forces crushed large street demonstrations, drawing international condemnation.