Background: The COVID-19 pandemic has put a tremendous burden on healthcare professionals, impacting various aspects of their psychological lives and well-being, including sleep quality. Prolonged sleep deprivation has been linked to burnout, which is increasingly recognized as a threat to patient safety. Our study aimed to assess sleep quality and burnout among health care workers (HCWs) during the COVID-19 pandemic. Methods: A cross-sectional study was conducted during the COVID pandemic from September to December 2021. The study participants were HCWs from three hospitals that dealt with the pandemic. A Google form was prepared and distributed to the target group. We used the Pittsburgh sleep quality index (PSQI) and the Maslach Burnout Inventory (MBI) to assess sleep quality and burnout, respectively. Results: The study included 257 HCWs; about three-fourths (73.5%) of them had poor sleep with an average PSQI score of 6.33 ± 2.07, while 29.2% of them had burnout. Poor sleep quality was significantly related to female gender, the presence of co-morbidities, working for more than 48 hours per week, frontline workers, and those who had family members or college students infected with COVID-19. Burnout was significantly associated with poor sleep. The total PSQI score was statistically significantly positively correlated with the MBI score (r = 0.5 and p-value = 0.001**). Conclusion: The COVID-19 pandemic had a significant impact on sleep quality among HCWs, which in turn contributed to burnout. Preventive interventions to promote good sleep quality and prevent burnout in HCWs during a healthcare crisis are essential.