The COVID-19 pandemic and the measures taken to contain it have substantial consequences for many people, resulting in negative effects on individual well-being and mental health. In the current study, we examined whether individual changes in perceived stress relative to pre-pandemic levels depended on differences in behavior, appraisal, and experience of pandemic-related constraints. In addition, we tested whether this potential relationship was moderated by personality traits. We conducted an online survey during the end of the first lockdown in Germany in spring 2020, and assessed pandemic-related individual consequences as well as perceived stress. These data were related to the big five personality traits and to ratings of perceived stress obtained from the same participants in a study conducted before the outbreak of the pandemic, using the same standardized stress questionnaires. There was no overall increase, but a large interindividual variety in perceived stress relative to pre-pandemic levels. Increased stress was associated especially with strong feelings of missing. This relationship was moderated by agreeableness, with more agreeable people showing a higher association of the feeling of missing and the increase of perceived stress. In addition, openness and conscientiousness were positively correlated with an increase in stress. The results highlight the importance of considering personality and individual appraisals when examining the consequences of the COVID-19 pandemic on perceived stress and well-being.