Background Nurses are at the frontline of care provision to patients with coronavirus disease 2019 (COVID-19). The high communicability of COVID-19, high levels of stress associated with the disease, and challenges of care provision to afflicted patients faced nurses in Iran with problems such as depression, anxiety, and stress. The aim of the study was to assess depression, anxiety, and stress among Iranian nurses who provided care to patients with COVID-19. Methods This cross-sectional descriptive-analytical study was conducted in 2020–2021. Participants were 468 nurses purposively selected from university hospitals in Iran. They completed two online instruments, namely a demographic questionnaire and the 21-item Depression Anxiety Stress Scale. Data were analyzed using the SPSS software (v. 23.0). Results Most participants were female (75.9%) and married (73.4%) and held bachelor’s degree (88%). The means of participants’ age and work experience were 33.59 ± 6.40 years and 10.26 ± 6.61 years, respectively. The mean scores and the prevalence rates of depression, anxiety, and stress were 13.56 ± 5.37 and 74.1%, 13.21 ± 4.90 and 89.7%, and 15.13 ± 4.76 and 54.9%, respectively. The prevalence rates of moderate to severe depression, anxiety, and stress were 43.7%, 73%, and 24%, respectively. The mean scores of participants’ depression, anxiety, and stress had significant relationship with their employment status (p < 0.05). Besides, the mean scores of their anxiety had significant relationship with their educational level, employment status, and work shift (p < 0.05). Conclusion Most nurses who provide care to patients with COVID-19 suffer from depression, anxiety, and stress. Psychological support services may be needed for nurses in order to protect and promote their mental health.