COVID-19 disease, caused by the SARS-CoV-2 virus, continues to cause high hospitalization and death rates. Vaccination campaigns have been key to controlling the pandemic, but vaccine hesitancy is on the rise. This study investigated the general population’s attitude to vaccination in Veneto (northeast Italy) in January 2021 as part of a study on the prevalence of SARS-CoV-2 infection. An ad hoc questionnaire collected 4467 respondents’ sociodemographic data and propensity to be vaccinated, and findings were analyzed using logistic multivariable regression. The 48.9% of respondents were male, and the mean age was 46.8 ± 16.0 years. Asked whether they would get vaccinated against COVID-19, 84.3% said yes, 5.0% were uncertain, and 10.7% said no. Vaccine acceptance was higher in males than in females (85.8% vs. 82.8%), in people 70+ years old (92.3%), and among people with more than 14 years of schooling (89.6%). Multivariable analysis with adjOR (95% CI) showed a significantly greater vaccine reluctance in females (0.68 (0.57–0.81)), people 30–49 or 50–69 years old (0.69 (0.54–0.87)), and (0.76 (0.58–0.99)); and those with <9 or 9–13 years of schooling (0.62 (0.46–0.82)), and (0.72 (0.57–0.91)). As people refusing vaccination undeniably hinder efforts to control the pandemic, specific strategies are needed to overcome their doubts.