Background Medical students’ psychological response to societal lockdown during the COVID-19 pandemic has not been studied much. Objective To assess levels of anxiety and depression among medical students during initial stages of COVID-19 pandemic in Nepal and relate their distress to relevant variables. Method A cross-sectional study with online questionnaire was conducted among medical students at different colleges in Nepal. Hospital Anxiety and Depression Scale (HADS) detected ‘anxiety’ and ‘depression’. The covariates were explored by logistic regression analyses. Result A total 416 medical students [mean age: 22.2 (2.1); males 57.7%, females 42.3%] participated. HADS-anxiety scores [mean: 7.1(4.3)] were significantly and positively correlated with HADS-depression [mean: 5.9 (4.1)] (r=0.695; p < 0.001). Point prevalence of total HADS caseness (HADS-T) was 26.7%. Specific HADS-defined caseness were: anxiety (HADS-A) 11.8%, depression (HADS-D) 5.5%, and comorbid anxiety and depression (HADS-cAD) 9.4%. All four types of caseness were significantly more prevalent among students with a history of mental problems (AOR=4.7, 3.2, 2.6, and 3.2 respectively). HADS-T was higher among those with a concurrent physical illness (AOR=2.4). HADS-T, HADS-A and HADS-D scores were higher among the age group > 22 years (AOR= 2.2, 2.5 and 4.4 respectively). HADS-cAD was almost three times higher among those with a possible COVID-19 exposure (AOR=2.8). Conclusion A significant number of medical students in Nepal suffered from high levels of anxiety and depression during the COVID-19 shut-down. The students in the higher (> 22 years) age group, those with past mental disorders, possible COVID-19 exposure, and concurrent physical illness showed elevated levels of anxiety and/or depression.