Objective To evaluate the anxiety and depression amid novel coronavirus disease-19 (COVID-19) pandemic in health sciences students around the globe. Materials and Methods This cross-sectional observational study comprised 523 health science students. A well-structured online questionnaire consisting of closed-ended questions based on student’s general information, Patient Heath Questionnaire (PHQ)-9 and Generalized Anxiety Disorder (GAD)-7 scales were used to assess the psychological impact of COVID-19. Statistical Analysis SPSS-25 was used to analyze the outcome of this study. Multiple linear regression analysis test was used to assess variables which had impact on PHQ-9 and GAD-7 scores among the participants. A p-value of ≤ 0.05 was considered as statistically significant. Results Among the 523 participants, 365 (69.55%) students were from developing countries and 158 (30.21%) from developed countries; 424 (81.1%) students were tested negative for COVID-19 and 99 (18.9%) had suffered from severe acute respiratory syndrome coronavirus 2 infection during pandemic. The mean GAD-7 and PHQ-9 scores were 7.16 ± 5.755 and 7.30 ± 6.166, respectively. Significant impact on anxiety levels was associated with age, gender, education status, and COVID-19 positive patient, while depression was not significantly associated with gender, COVID-19, and its reported symptoms in participants. Conclusion As the world is trying to contain the health effects of COVID-19, the psychological effects might take a longer time to be addressed. Our study highlights the dire need to identify mental well-being of health science students as this may have a direct impact on their professional commitments and future responsibilities.