Background The COVID-19 pandemic has been creating a panic and distressing situations among the entire population globally including Nepal. No study has been conducted assessing the psychological impact of this pandemic on the general public in Nepal. The objective of this study is to assess the mental health status during COVID-19 outbreak and explore the potential influencing factors among the population attending the hospital fever clinics with COVID-19 symptoms. Methods A cross-sectional survey was conducted between May-June, 2020 with a sample of 645 participants aged 18 and above in 26 hospitals across Nepal. Telephone interviews were conducted using a semi-structured questionnaire along with a validated psychometric tool, the Depression, Anxiety and Stress (DASS-21) scale. The metrics and scores of symptoms and their severity were created and analyzed. Multivariate logistic regression was used to determine the association of potential covariates with outcome variables. Results The prevalence of anxiety, depression and stress were 14%, 7% and 5% respectively. In reference to Karnali, participants from Bagmati province reported higher level of anxiety (OR 3.44, 95% CI 1.31-9.06), while stress (OR 4.27, 95% CI 1.09-18.32) and depressive symptoms (OR 3.11, 95% CI 1.05-9.23) observed higher among the participants in Province 1. Women were more at risk of anxiety (OR 3.41, 95% CI 1.83-6.36) than men. Similarly, people currently living in rented houses reported more stress (OR 2.97, 95% CI 1.05-8.43) and those living far from family reported higher rates of depressive symptoms (OR 3.44, 95% CI 1.03-11.46). Conclusion The study identified increased prevalence of stress, anxiety and depressive symptoms during the initial stage of COVID-19 pandemic in Nepal. Considering the findings, there is urgent need to develop and implement appropriate community-based mental health programs targeting individuals who have had COVID-19 symptoms and who are prone to develop adverse mental health outcomes.