At the heart of the unparalleled crisis of COVID-19, healthcare workers (HCWs) face several challenges treating patients with COVID-19: reducing the spread of infection; developing suitable short-term strategies; and formulating long-term plans. The psychological burden and overall wellness of HCWs has received heightened awareness in news and research publications. The purpose of this study was to provide a review on current publications measuring the effects of COVID-19 on wellness of healthcare providers to inform interventional strategies. Between April 6–May 17, 2020, we conducted systematic searches using combinations of these keywords and synonyms in conjunction with the controlled vocabulary of the database: “physician,” “wellness, “wellbeing,” “stress,” “burnout,” “COVID-19,” and “SARS-CoV-2.” We excluded articles without original data, research studies regarding the wellness of non-healthcare occupations or the general public exclusively, other outbreaks, or wellness as an epidemic. A total of 37 studies were included in this review. The review of literature revealed consistent reports of stress, anxiety, and depressive symptoms in HCWs as a result of COVID-19. We describe published data on HCW distress and burnout but urge future research on strategies to enhance HCW well-being.