This study investigated changes in the prevalence of depression, stress, and suicidal attempts during the COVID-19 pandemic. The ≥19-year-old population in the Korea National Health and Nutrition Examination Survey in 2019 and 2020 was included. The histories of depression, stress, and suicidal attempts were compared between the 2019 and 2020 cohorts using multiple logistic regression analysis with complex sampling. The prevalence of depression was not significantly different between the 2019 and 2020 groups (4.1% vs. 4.5%, p = 0.326). The prevalence of stress and suicide attempts was also not significantly different between groups (all p > 0.05). The rates of depression, stress, and suicide attempts were not associated with the 2020 group compared to the 2019 group (all p > 0.05). The 19- to 39-year-old group in the 2020 group indicated a higher rate of depression (diagnosed by physicians) than the 19- to 39-year-old group in the 2019 group (adjusted odds ratio = 1.58, 95% confidence intervals = 1.00–2.50, p = 0.049). The risks of depression, stress, and suicidal attempts were not related to the COVID-19 pandemic in Korean adults. A young adult population demonstrated an increased risk of depression associated with the COVID-19 pandemic.