Uptake of a vaccine is complete if individuals are aware of the associated risks of the vaccine, accept the vaccine, and respond positively to the nudges (activation) to increase the uptake, and respond when the vaccine is made accessible and affordable. We mapped systematically the existing literature concerning the 5As-acceptability, accessibility, affordability, awareness, and activation-of COVID-19 vaccination among adults and, specifically, older adults (55 years and older) in Africa. We searched multiple databases from 2020 to December 2021. Using predefined inclusion and exclusion criteria, two reviewers screened citations, conducted title and abstract screening, and extracted data independently. We included 68 articles conducted in 33 African countries, primarily cross-sectional studies (n = 49, 72%). None of the articles focused on older adults only, but 22 articles (32%) included at least one older adult (55 years and older) in their sample size. Acceptance (n = 58, 85%) was the most commonly researched aspect of vaccine uptake, followed by accessibility (n = 17, 25%), awareness (n = 13, 19%), and affordability (n = 5, 7.0%). We found only one report on activation. Factors affecting acceptance of the COVID-19 vaccine in Africa were grouped into sociodemographic factors; knowledge-, attitude-, and belief-related factors; a COVID-19 vaccine efficacy and safety concern factor; and trust in government and public health authorities. The governments of African nations should focus on strategies to influence the modifiable factors identified in this review. More studies are needed to evaluate the impact of nudges (activation) to improve COVID-19 vaccine uptake in African nations.