Background Emotional wellbeing of healthcare workers is critical to the quality of patient care, and effective function of health services. The corona virus disease-2019 (COVID-19) pandemic exerted unique physical and emotional demands on healthcare workers, however little is known about the emotional wellbeing of healthcare workers during the COVID-19 pandemic in resource-restricted settings. This study investigated the prevalence of psychological distress, and sleep problems in healthcare workers in a COVID-19 referral hospital in Nigeria. Methods A total of 303 healthcare workers were interviewed with the 12-item General Health Questionnaire (GHQ-12) to evaluate psychological distress, and the Pittsburgh Sleep Quality Index (PSQI) to assess multidimensional aspects of sleep, including quality, latency, duration, habitual efficiency, disturbances, use of sleeping medications and daytime dysfunction. Results The participants were mostly males, 183(60.4%) and mean age was 38.8(SD = 8.9) years. Most of the participants were married (70.3%), had spent less than 10 years in service (72.9%), and had no medical comorbidity (92.1%). The prevalence of psychological distress was 23.4%, and six in every ten participants reported sleep problems. The largest proportion of participants reported difficulty in sleep latency (81.5%), duration (71.3%), and daytime dysfunction (69.6%), while approximately one third (32%) each reported using sleep medication, and had difficulty with sleep quality. Psychological distress was inter-related with poor sleep problems ( p = 0.001; effect size = 0.2). Conclusion The prevalence rates of psychological distress and sleep problems during the COVID-19 pandemic were several folds the rates previously reported in similar contexts. Preventative psychosocial support services for healthcare workers are indicated. The creation of a culturally-sensitive interdisciplinary blueprint for locally-viable actions model are strongly suggested ahead of future emergency situations.