Vaccinations are proven to be the most efficient in preventing COVID-19 disease. Nonetheless, some people are skeptical and hesitant. The study aimed to determine factors associated with willingness to receive a COVID-19 vaccine in the Polish adult population. An online survey consisting of questions regarding (1) demographic information and (2) health issues (the status of vaccination, comorbidities, receiving the flu vaccine and usage of health monitoring apps) was distributed between 13 January and 14 February 2022. Of the 7018 participants who met the study conditions, 76.89% (n = 5396) were females, 22.44% (n = 1575) were males and 0.67% (n = 47) did not specify gender. The median age was 31 years. Among them, 81.82% (n = 5742) were vaccinated and 18.18% (n = 1276) were not. 46.87% (n = 3289) had no chronic co-morbidities. Factors associated with lower odds to receive the vaccine were: being men (p = 0.02; OR = 0.83), having lower education status (p = 0.001, OR = 0.56–0.77), living in a smaller residence area (p < 0.001, OR = 0.47–0.73.), not receiving flu vaccination (p < 0.001, OR = 24.51) and not using health monitoring applications (p < 0.001, OR = 1.56). Health education and communication strategies are needed to achieve large-scale vaccine acceptability and finally herd immunity.