Objective: This study examined the factors affecting depression, anxiety, and suicidal ideation among patients with coronavirus disease-2019 (COVID-19) during the early phase of COVID-19 in South Korea and investigated the role of stigma in moderating the effects of loneliness on mental health problems among these patients. Methods: Conducted as part of the COVID-19 Mental Health Panel Survey over 12 weeks in 2021, this survey enrolled participants aged 15–79 years, applying standardized weights for ratio correction, and collected 640 completed questionnaires. Demographic characteristics were analyzed using descriptive statistics. Suicidal ideation, anxiety, and depression post-COVID-19 were examined using t-tests and logistic regression. The PROCESS macro explored stigma’s moderating effects on loneliness and mental health outcomes. Results: Results showed that 7.9% and 10.0% of the enrolled participants were at risk for anxiety and depression, respectively, with 3% contemplating suicide post-COVID-19. Stigma positively impacted depression and anxiety, acting as a significant moderator for loneliness, and mental health, with a stronger effect for higher stigma perception. Unemployment and college education elevated mental health risks in COVID-19 cases. Low health satisfaction and poor sleep were linked to suicidal ideation, while fatigue and COVID-19 stigma increased depression and anxiety risks. Loneliness was significantly associated with suicidal ideation, depression, and anxiety. Conclusion Unemployment, college education, low health satisfaction, and poor sleep were linked to suicidal ideation. Fatigue and COVID-19 stigma raised depression/anxiety risks. Loneliness correlated with suicidal thoughts, depression, and anxiety. Stigma moderated the link between loneliness and mental health issues.