Fees had been frozen last year after the biggest student protests since the end of apartheid in 1994.
The demonstrators say price increases discriminate against black students with low family incomes.
The University of Bloemfontein and the Nelson Mandela Metropolitan University in the coastal city of Port Elizabeth said they had closed campuses because of the protests.
The University of Cape Town announced the suspension of classes as students sang revolutionary songs barricaded entrances with litter bins. University of Witwatersrand Students' Representative Council leader Nompendulo Mkatshwa police fired stun grenades at students who had gathered near the university to protest against the proposed fee increase.
"Students are not happy with what the Department of Higher Education and Training said, so they are fighting for equal education," Ms Mkatshwa is quoted by Reuters news agency as saying.
Police spokesman Lungelo Dlamini said the arrested students "were blocking the entrance of the university in contravention of the court order" and were being held at a nearby station, Reuters reports.
The freeze has now been lifted, with Higher Education Minister Blade Nzimande announcing on Monday that universities will be allowed to increase fees by a maximum of 8%.
Critics say this is higher than the 6% inflation rate, and will make university education unaffordable for many students. However, universities favour an increase, saying they were facing a financial crisis which was damaging their academic programmes.