•COVID-19-related anxiety was positively associated with vaccine acceptance.•Health-related fears correlated positively with vaccine acceptance.•Social and economic fears were negatively associated with vaccine acceptance.•Distinguishing between different types of fears and anxiety seems to be important.•Acceptance differed between users/non-users of social and official media formats. Vaccination is crucial to limit the pandemic spread of SARS-CoV-2/COVID-19. Therefore, besides the development and supply of vaccines, it is essential that sufficient individuals are willing to get vaccinated, but concerning proportions of populations worldwide show vaccine hesitancy. This makes it important to determine factors that are associated with vaccine acceptance. 1779 adults of a non-probability convenience sample in Germany were assessed with an online survey in a cross-sectional survey period from 1st to 11th January 2021 (a few days after the beginning of vaccinations in Germany). 64.5% of the sample stated that they absolutely would accept the vaccination, 13.8% would rather accept it, 10.4% were undecided, and 5.2% would rather not and 6.0% absolutely not get vaccinated. COVID-19-related anxiety, and fears of infection and health-related consequences correlated significantly positively with vaccine acceptance (all p < .001). In contrast, social (p = .006) and economic fears (p < .001) showed significant negative associations with vaccination willingness. The broader constructs of unspecific anxiety and depressive symptoms were not significantly associated with vaccine acceptance. Vaccine acceptance differed between users/non-users of social media and official websites to gain information about the pandemic (p < .001). COVID-19-related anxiety and health-related fears were associated with higher vaccine acceptance, whereas the fear of social and economic consequences showed the contrary direction. These findings highlight the need to differentiate between several types of fears and anxiety to predict their influence on vaccine acceptance, and provide important information and an essential base for future studies and interventions.