The violence was sparked after a large area, including Lubumbashi university, was left without water and electricity for three days because of damage caused to vital cables and pipes by torrential rains.
The students were also demonstrating over higher fees, Presstv Reported.
Clashes broke out on Sunday after police used tear gas and warning shots to try to disperse crowds of students returning from the governor's residence in Upper Katanga.
"The provisional figures established by officials report four deaths, including three students and a policeman," said Vital Kamerhe, chief of staff of new president Felix Tshisekedi, in a statement.
Tshisekedi was sworn in last Thursday, marking DR Congo's first peaceful handover of power but only after chaotic and bitterly disputed elections.
Runner-up Martin Fayulu has dismissed the result as a stitch-up between Tshisekedi and outgoing president Joseph Kabila, who ruled DR Congo for 18 years.
The police officer who "ordered to shoot the peaceful students without warning" will be brought before a military court "to face the rigor of the law," the statement said.
It added that increases to academic fees paid by the university's 10,000 students had been "suspended."
Water and electricity supplies have been restored to the university campus, according to students.
Earlier police reports had said one student was shot dead and a police officer died after being hit by an anti-riot vehicle.