There has been a lack of information on vaccine acceptance for Finnish adults. We conducted a secondary analysis of cross-sectional data collected through the Finnish Medicines Agency Medicine Barometer 2021 survey (response rate: 20.6%). We described and explained vaccine acceptance by investigating the associations between socio-demographic factors and statements using logistic regression and conducted a factor analysis. The majority of respondents (n = 2081) considered vaccines to be safe (93%), effective (97%), and important (95%). However, 20% and 14% felt they did not have enough information about vaccines and vaccine-preventable diseases (VPDs), respectively. Respondents aged 18–39 were 2.8 times more likely to disagree that they had enough information about VPDs compared to respondents aged 60–79 (p < 0.001), while respondents with poorer self-perceived health were 1.8 times more likely to declare not having enough information about vaccines (p < 0.001). We generated three-factor dimensions from the eight statements. They were related to ‘Confidence and attitudes towards vaccines’, ‘Access to information on vaccines and VPDs’, and ‘Debate on vaccine issues’, which may reflect the underlying thinking patterns. Access to and understanding of information about vaccines and VPDs need to be improved for Finnish adults to increase vaccine acceptance and uptake, thus preventing the spread of VPDs.