Background: The global outbreak of COVID-19 has created unprecedented havoc among health care workers, resulting in significant psychological strains like insomnia. This study aimed to analyze insomnia prevalence and job stressors among Bangladeshi health care workers in COVID-19 units. Methodology: We conducted this cross-sectional study to assess insomnia severity from January to March 2021 among 454 health care workers working in multiple hospitals in Dhaka city with active COVID-dedicated units. We selected 25 hospitals conveniently. We used a structured questionnaire for face-to-face interviews containing sociodemographic variables and job stressors. The severity of insomnia was measured by the Insomnia Severity Scale (ISS). The scale has seven items to evaluate the rate of insomnia, which was categorized as the absence of Insomnia (0–7); sub-threshold Insomnia (8–14); moderate clinical Insomnia (15–21); and severe clinical Insomnia (22–28). To identify clinical insomnia, a cut-off value of 15 was decided primarily. A cut-off score of 15 was initially proposed for identifying clinical insomnia. We performed a chi-square test and adjusted logistic regression to explore the association of different independent variables with clinically significant insomnia using the software SPSS version 25.0. Results: 61.5% of our study participants were females. 44.9% were doctors, 33.9% were nurses, and 21.1% were other health care workers. Insomnia was more dominant among doctors and nurses (16.2% and 13.6%, respectively) than others (4.2%). We found clinically significant insomnia was associated with several job stressors (p < 0.05). In binary logistic regression, having sick leave (OR = 0.248, 95% CI = 0.116, 0.532) and being entitled to risk allowance (OR = 0.367, 95% CI = 0.124.1.081) showed lower odds of developing Insomnia. Previously diagnosed with COVID-19-positive health care workers had an OR of 2.596 (95% CI = 1.248, 5.399), pointing at negative experiences influencing insomnia. In addition, we observed that any training on risk and hazard increased the chances of suffering from Insomnia (OR = 1.923, 95% CI = 0.934, 3.958). Conclusion: It is evident from the findings that the volatile existence and ambiguity of COVID-19 have induced significant adverse psychological effects and subsequently directed our HCWs toward disturbed sleep and insomnia. The study recommends the imperativeness to formulate and implement collaborative interventions to help HCWs cope with this crisis and mitigate the mental stresses they experience during the pandemic.