Background: Coronavirus disease-2019 (COVID-19) in the last few months has disrupted the healthcare system globally. The objective of this study is to assess the impact of the COVID-19 pandemic on the psychological and emotional well-being of healthcare workers (HCWs). Materials and methods: We conducted an online, cross-sectional, multinational survey, assessing anxiety [using Generalized Anxiety Disorder (GAD) Scale: GAD-2 and GAD-7], depression (using Center for Epidemiologic Studies Depression Scale), and insomnia (using Insomnia Severity Index Scale), among HCWs across India, the Middle East, and North America. We used univariate and bivariate logistic regression to identify risk factors for psychological distress. Results: The prevalence of clinically significant anxiety, depression, and insomnia was 41.4%, 48.0%, and 31.3%, respectively. On bivariate logistic regression, lack of social or emotional support to HCWs was independently associated with anxiety [odds ratio (OR), 3.81 (2.84–3.90)], depression [OR, 6.29 (4.50–8.79)], and insomnia [OR, 3.79 (2.81–5.110]. Female gender and self-COVID-19 were independent risk factors for anxiety [OR, 3.71 (1.53–9.03) and 1.71 (1.23–2.38)] and depression [OR, 1.72 (1.27–2.31) and 1.62 (1.14–2.30)], respectively. Frontliners were independently associated with insomnia [OR, 1.68 (1.23–2.29)]. Conclusion: COVID-19 pandemic has a high prevalence of anxiety, depression, and insomnia among HCWs. Female gender, frontliners, self-COVID-19, and absence of social or emotional support are the independent risk factors for psychological distress.