Fastjet said Mark Hurst, its deputy group chief executive officer, would lead the airline until a permanent replacement was appointed.
Bezuidenhout could not be reached immediately for comment.
Media reports last month suggested that Bezuidenhout could return to Mango Airlines as its top boss, a role he previously held for nearly a decade.
The airline, which operates in South Africa, Mozambique and Zimbabwe, has faced several issues related to its dwindling cash pile and was saved from going under after striking a deal to raise funds late last year.
Bezuidenhout told Reuters last week that Fastjet was expected to be profitable on an underlying basis by the end of 2019.