Aim The new coronavirus disease (COVID-19) pandemic has laid unprecedented stress on healthcare workers and especially nurses. The main objective of this study is to determine the prevalence of stress, anxiety, depression and sleep disturbance among nurses in Oman during the COVID-19 pandemic, and to explore the contributing factors. Methods A cross-sectional and descriptive correlational design using Qualtrics® software was performed. Data were collected using the Pittsburgh Sleep Quality Index, the Hospital Anxiety and Depression Scale and the Perceived Stress Scale. Results Of the 1,130 nurses who participated, 75.6% (n = 854) reported stress, 44.2% (n = 499) reported anxiety, 38.5% (n = 435) reported depression and 73.7% (n = 833) reported poor sleep. Stress, anxiety, depression and sleep disturbance (p < .05) were significantly associated with age, marital status, comorbidity and whether family members or relatives were suspected or confirmed with COVID-19. The stress, anxiety, depression and sleep disturbance were significantly positively corelated with each other. Logistic regression showed nurses in the age group between 18 and 30, who worked at the frontline, were at a higher risk of stress, anxiety, depression and sleep disturbance. Conclusions Stress, anxiety, depression and sleep disturbance are significant problems for nurses working in Oman during the COVID-19 pandemic. Appropriate interventions to monitor and reduce psychological problems and sleep disturbance among nurses are needed, which can help to support nurses’ work during contagious disease outbreaks.