Kiir issued the order after meeting South Sudan's Minister of Higher Education, Gabriel Changson Chang, and Minister of Finance and Economic Planning, Dier Tong Ngor, this week.
Rumbek University Vice Chancellor Deng Manassi Mach stressed to VOA that lecturers at his institution would not teach students until the government paid their salary arrears.
"The academic staff have [laid] down their tools and I have tried to talk to the Ministry of Finance they have not yet responded, definitely this will affect the academy year and timetable for the examination too." Mach said.
In January Kirr ordered South Sudan's Ministry of Education to increase the salaries of lecturers at public universities by 300%, lecturers say they have not been paid since the new salary structure was ordered.
Tieng Tanich, information secretary at Rumbek University, told VOA that lecturers are also demanding salary arrears dating back four years.
He said members of the staff at the university are determined to stay off the job until the government fulfills their demands.
"Today there is nobody at the Rumbek University premises due to the strike and our strike is not violence, but it is to get our right(s) and we have been patient for the Ministry of Finance to pay us since the day that the new salary structure bill was passed." Tanich said.
The board of the University of Juba, the country's oldest institution, also issued a statement this week supporting the move taken by public universities to suspend all teaching until the finance ministry pays salaries of the lecturers.
Dhieu William, a teacher at the University of Juba, said lecturers have no other jobs to supplement their incomes, adding that the government should look in the demands of lecturers.
"I think it is our right. The strike by the lecturers is right because it will push the Ministry of finance to pay the salaries and as we go on strike the students will be affected," William said.
Charles Aligo Albert, a third-year student of medicine at the University of Juba said the strike has affected his studies.
"We have just started only a month and it will affect us and at the end we shall be having exams and it is not going to be okay," Albert said.
"I want the government to discuss with the lecturers and adjust the salary to be on time and let them solve the issue," he added.