The COVID-19 pandemic has spiked stress-related symptoms worldwide. This study aims to assess depressive symptoms related to the early phase of the COVID-19 outbreak among the Italian general population and to analyze anhedonia and emotion dysregulation as potential predictors of depression severity. Through an online questionnaire, we collected sociodemographic and lockdown-related information; depressive symptoms, hedonic tone, and emotion dysregulation were assessed through the Beck Depression Inventory II, the Snaith–Hamilton Pleasure Scale, and the Difficulties in Emotion Regulation Scale, respectively. In our sample (n = 500), 122 individuals (24.4%) reported depressive symptoms during the COVID-19 outbreak. Individuals with and without depression differed in gender (X2 = 4.77, df = 1, p = 0.02) and age (X2 = 15.7, df = 4, p = 0.003). Among individuals presenting with depressive symptoms, those reporting close contact with confirmed cases of COVID-19 were at higher risk for severe depression (p = 0.026). Reduced hedonic tone (p = 0.014) and emotion dysregulation (p < 0.001) also predicted depression severity. To the best of our knowledge, these are among the earliest data that focus on the risk for depression among a sizeable sample of the Italian general population during the COVID-19 outbreak. Our results indicate emotion dysregulation and reduced hedonic tone as potential factors predicting COVID-19-related depression severity and provide insight into developing targeted intervention policies.