The COVID-19 pandemic revealed that health denialism might be an important determinant of adherence to preventive measures during epidemic challenges. Conspiracy beliefs seem to be one of the most visible manifestations of denialism in society. Despite intensive efforts to promote COVID-19 vaccinations, the number of citizens reluctant to get vaccinated was very large in many countries. The main aim of this study was the analysis of the association between the acceptance of the COVID-19 vaccination and conspiracy beliefs among adult Internet users in Poland. The analysis was based on data from a survey performed on a sample of 2008 respondents in October 2021. Uni- and multivariable logistic regression models were applied to evaluate the association between attitudes towards COVID-19 vaccination and generic conspiracist, vaccine-conspiracy, and COVID-19-related conspiracy beliefs. In the multivariable model, the effect of conspiracy beliefs was adjusted for the level of vaccine hesitancy, future anxiety, political sympathies, and socio-demographic variables. Univariate regression models showed that COVID-19 vaccination acceptance is significantly lower among respondents with higher levels of all three types of conspiracy beliefs. In the multivariable model, the effect of COVID-19-related and vaccine conspiracy beliefs, but not generic conspiracist beliefs, was maintained after adjusting for vaccine hesitancy. We conclude that conspiracy beliefs should be treated as a potential indicator of lower adherence to preventive measures during epidemic challenges. The respondents revealing a high level of conspirational thinking are a potential group for intensified actions which employ health educational and motivational interventions.