Due to the rapid development of COVID-19 vaccines, the world has faced a huge challenge with their general acceptance, including Poland. For this reason, we attempted to determine the sociodemographic factors influencing the decision of positive or negative attitudes toward COVID-19 vaccination. The analysis included 200,000 Polish participants—80,831 women (40.4%) and 119,169 men (59.6%). The results revealed that the most common reasons for vaccine refusal and hesitancy were the fear of post-vaccination complications and their safety (11,913/31,338, 38.0%; 9966/31,338, 31.8%). Negative attitudes were observed more often among male respondents with primary or secondary education (OR = 2.01, CI95% [1.86–2.17] and OR = 1.52, CI95% [1.41–1.63], respectively). On the other hand, older age ≥ 65 (OR = 3.69; 95%CI [3.44–3.96]), higher education level (OR = 2.14; 95%CI [2.07–2.22]), living in big cities with a range of 200,000–499,999 inhabitants and more than 500,000 inhabitants (OR = 1.57, CI95% [1.50–1.64] and OR = 1.90, CI95% [1.83–1.98], respectively), good physical conditions (OR = 2.05; CI95% [1.82–2.31]), and at last normal mental health conditions (OR = 1.67, CI95% [1.51–1.85]) were significantly associated with COVID-19 vaccine acceptance. Our study indicates which population group should be further supplied with data and information by health education, the government, and healthcare professionals to alleviate the negative attitude toward COVID-19 vaccines.