Objective: As COVID-19 continues to spread, researchers are working to develop a safe and effective vaccine. The success of an approved vaccine in stopping or slowing the pandemic will ultimately depend on the public’s acceptance of it. As studies indicate that people perceive COVID-19 as a threatening disease, the demand for a vaccine could be expected to be high. However, vaccine safety concerns might still outweigh the perceived disease risks in a decision to vaccinate against COVID-19. In the present paper, the role of perceived risk of COVID-19 (i.e., perceived likelihood of infection, perceived disease severity, and disease-related worry) and trust in the safety of a prospective vaccine against COVID-19 in predicting intentions to accept a COVID-19 vaccine was investigated. Methods: Three Finnish samples were surveyed: 856 parents of small children, 205 individuals living in an area with suboptimal vaccination coverage, and 1,325 Facebook users nationwide. As points of reference, we compared the perceptions of COVID-19 to those of influenza and measles. Results: COVID-19 was perceived as a threatening disease—more so than influenza and measles. The strongest predictor of COVID-19 vaccination intentions was trusting the safety of the potential vaccine. Those perceiving COVID-19 as a severe disease were also slightly more intent on taking a COVID-19 vaccine. Conclusions: If a vaccine against COVID-19 is successfully developed, assuring the public that the vaccine is safe should be the focus for health authorities aiming to achieve a high vaccine uptake.