Background: Increased acceptance and uptake of Coronavirus Disease 2019 (COVID-19) vaccines is very essential in containing the ongoing COVID-19 pandemic. Vaccine hesitancy is a threat to public health containment of infectious diseases. Aim: The main aim of this study was to review published articles regarding COVID-19 vaccine acceptability and hesitancy across all populations in Africa. Materials and methods: This was a narrative review. A comprehensive literature search was done using PubMed, Google Scholar, Scopus, and EMBASE using the keywords vaccine acceptability, vaccine hesitancy, COVID-19 vaccine, COVID-19 pandemic, H1N1 vaccine, swine flu, swine flu vaccine, Africa, and the Boolean word AND. The cited literature was published between March 2001 and June 2021. Results: The few studies were done in Africa so far are among healthcare workers and medical students. Acceptance of vaccination against COVID-19 in Africa ranged from 15.4% to 55.9%. This shows increased hesitancy to receive the COVID-19 vaccines in African countries. Many people were concerned about the potential adverse effects and ineffectiveness of COVID-19 vaccines. Misinformation about the COVID-19 vaccines has contributed to the hesitancy reported from different studies. Moreover, sociodemographic characteristics were also predictors of the acceptability of COVID-19 vaccines. Conclusion: Low acceptability rates reported in Africa indicates increased hesitancy to vaccination against COVID-19. The low acceptance of vaccines in Africa can hinder the required 60-70% vaccinations to achieve herd immunity. Therefore, there is a need to develop strategies that will address hesitancy against the COVID-19 vaccines across countries and populations in Africa and the entire globe.