Coronavirus disease (COVID-19) is a global public health problem that has had a detrimental influence on the economy of countries of the world, including Nigeria: (1) Background: The study aimed to assess COVID-19 vaccine acceptance and hesitancy among staff and students at Federal University of Health Sciences Otukpo, Benue State, Nigeria, while exploring the factors influencing these attitudes; (2) Methods: A web-based cross-sectional survey was conducted between November 2021 and April 2022, with data analyzed using descriptive and inferential statistics; (3) Results: Of the hundred and fifty (150) completed and analysed questionnaires the mean age of the respondents was 34.8 ± 8.64 years, of which majority of them 80.0% (122) ranging between 16 and 45 years. The majority of the respondents 77.3% (116) have been tested for the virus to know their status. In total, 51.2% of trial participants indicated hesitancy to get the COVID-19 vaccine. The two most frequent reasons for hesitation were scepticism about the vaccination due to fast production and rollout (32.2%) and fear of vaccine side effects due to social media movements (23.3%). The most often cited reasons for not receiving the COVID-19 vaccination included uncertainty about its efficacy, a lack of knowledge about the vaccine, a preference for another kind of protection, and unreliability of the vaccine (due to its rapid development). Staff category (Academics, non-academics, students, and health workers), age, and religion were the significant associated factors influencing vaccine acceptance and hesitancy (P < 0.05); (4) Conclusions: The university community has a high level of awareness of COVID-19 pandemic but vaccine acceptance is low resulting high levels of vaccine hesitancy. These findings suggest that there is a need for further information and education on the COVID-19 vaccine, particularly in communities where vaccine hesitancy is prevalent. This can be achieved through targeted outreach programs, community engagement initiatives, and effective communication strategies that address the concerns and questions of individuals who are hesitant about receiving the vaccine.