Background As a way of minimising the devastating effects of the coronavirus disease 2019 (COVID-19) pandemic, scientists hastily developed a vaccine. However, the scale-up of the vaccine is likely to be hindered by the widespread social media misinformation. We therefore conducted a study to assess the COVID-19 vaccine hesitancy among Zimbabweans. Methods We conducted a descriptive online cross-sectional survey using a self-administered questionnaire among adults. The questionnaire assessed willingness to be vaccinated; socio-demographic characteristics, individual attitudes and perceptions, effectiveness and safety of the vaccine. Multivariable logistic regression analysis was utilized to examine the independent factors associated with vaccine uptake. Results We analysed data for 1168 participants, age range of 19–89 years with the majority being females (57.5%). Half (49.9%) of the participants reported that they would accept the COVID-19 vaccine. Majority were uncertain about the effectiveness of the vaccine (76.0%) and its safety (55.0%). About half lacked trust in the government’s ability to ensure availability of an effective vaccine and 61.0% mentioned that they would seek advice from a healthcare worker to vaccinate. Chronic disease [vs no chronic disease—Adjusted Odds Ratio (AOR): 1.50, 95% Confidence Interval (CI)I: 1.10–2.03], males [vs females—AOR: 1.83, 95%CI: 1.37–2.44] and being a healthcare worker [vs not being a health worker—AOR: 1.59, 95%CI: 1.18–2.14] were associated with increased likelihood to vaccinate. Conclusion We found half of the participants willing to vaccinate against COVID-19. The majority lacked trust in the government and were uncertain about vaccine effectiveness and safety. The policy makers should consider targeting geographical and demographic groups which were unlikely to vaccinate with vaccine information, education and communication to improve uptake.