Evidence suggests that quarantine might have a wide-ranging, substantial, and long-lasting negative psychological impact especially when the necessary preventive measures are not taken. This study assessed the prevalence and associated factors of depression and anxiety among quarantined population during the COVID-19 outbreak in central Ethiopia. A community-based cross-section study was conducted among individuals under quarantine from June 5 to July 5, 2020, in Addis Ababa, Ethiopia. The hospital Anxiety and Depression Scale (HADS) was used to assess depression and anxiety. Binary logistic regression analysis (multivariate analysis) was used to identify the potential determinants of depression and anxiety. A total of 297 participants were included in the study which makes the response rate 90.8%. The prevalence of anxiety, depression, and co-morbid anxiety and depression were 21.5%, 70.7%, and 15.8% respectively. In our multivariable analyses, stressful life events (AOR 2.61, 95%CI (1.46, 4.67)), spent time on sleeping (AOR 1.97, 95% CI (1.08, 3.62)), and believing that COVID-19 could be prevented by wearing a glove (AOR 0.30, 95% CI (0.11, 0.81)) showed a statistically significant association with anxiety, whereas being married (AOR 2.67, 95% CI (1.37, 5.22)), had stressful life event in the last six months (AOR 1.44, 95% CI (1.44, 5.25)) and spending of time by sleeping during the quarantine (AOR 1.97, 95% CI (1.42, 6.19)) predicted depression. In conclusion, the current study result indicated that a considerable proportion of individuals who were under quarantine during the COVID-19 pandemic have experienced psychological disturbances, such as anxiety and depression. The results suggest that attention needs to be given to mitigate mental health problems in the quarantined population during the COVID-19 outbreak.