The Daily Dispatch Online reports in total, the four universities received 76,966 applications for 16,767 places, turning away 60,199 prospective students.
The numbers were provided by the Walter Sisulu University (WSU), Nelson Mandela Metropolitan University, Rhodes University and the University of Fort Hare.
The Dispatch Online reported the WSU had a handful of places open for national diplomas in information technology and accounting, which required advanced mathematics, but every other place in the province was taken.
The only places still available for first year students were for national diplomas in information technology and accounting, said WSU spokeswoman Angela Church.
"The minimum entry requirement for both is level four in mathematics and accounting. All other programmes are full and have waiting lists."
She said the university received 22,000 first-year applications, but could only accommodate 6329 students.
A Green Paper on proposals to overhaul the education system was released earlier this month by Higher Education Minister Blade Nzimande.
The paper is aimed at changing the post-school education system by increasing university enrolment and expanding Further Education and Training Colleges.
In January, a woman was killed in a stampede at the University of Johannesburg, where prospective students were queuing for last-minute applications.