The coronavirus disease 2019 (COVID-19) pandemic has had a significant impact on individuals’ mental health. This study aimed to investigate how negative emotions toward the COVID-19 pandemic, including feeling anxious, depressed, upset, and stressed, were associated with COVID-19 vaccine acceptance in Sweden. The study is a cross-sectional online survey conducted between 21–28 May 2021, using three nested hierarchical logistic regression models to assess the association. The study included 965 unvaccinated individuals, 51.2% (n = 494) of whom reported their intention to get vaccinated. We observed graded positive associations between reported negative emotions and vaccine acceptance. Individuals who experienced economic stress had lower odds of vaccine acceptance while having a positive opinion of the government’s response to COVID-19 was associated with higher odds of being vaccine-acceptant. In conclusion, unvaccinated individuals experiencing negative emotions about the pandemic were more willing to get the vaccine. On the contrary, those with a negative opinion about the government’s response, and those that had experienced economic stress were less likely to accept the immunization.