They had fabricated exam results, as well as other issues, said Higher Education Minister Blade Nzimande.
The institutions have failed to submit audited financial statements since 2020, the education department said.
Educor is yet to respond to a BBC inquiry about the allegations.
It runs educational institutions on more than 60 campuses in South Africa and internationally.
Damelin, CityVarsity, Icesa City Campus, and Lyceum College across the country must shut down by year-end.
Minister Nzimande informed journalists of serious issues uncovered during a large-scale college investigation.
Mr Nzimande labelled the colleges “dysfunctional” due to a number of complaints received from students and workers, “most of which remain unresolved”.
Some students complained about the poor quality of teaching and learning, lack of administrative support and lack of professionalism, the minister said.
There have been allegations of non-payment of staff salaries and corruption, he added.
The Educor institutions also inflated their numbers so as to hide their declining student population, according to the minister.
The provider said it had 50,000 students, however its 2022 annual reports indicate a total enrolment of 13,096 students across all four institutions, he said.
Mr Nzimande also said that some students’ examination marks were fabricated.