Introduction COVID-19 has had an important effect on nursing students, with some having their clinical practice cancelled or suspended and others suffering from the virus. Objective The purpose of this study was to assess the psychological status in terms of stress, anxiety, and depression of nursing students during COVID-19 pandemic. Methods The study was cross-sectional, carried out by a convenience sample of 320 participants of nursing students between May and June 2020. Data collection was performed by “Depression Anxiety Stress-21 Scale” (DASS-21). Results The results revealed that 78 (24.3%) of participants reported stress; 121 (37.8%) reported anxiety; and 72 (22.5%) reported depression. Also, grade and socioeconomic status had statistically significant effect on anxiety, stress, and depression. In addition, age had statistically significant effect on depression, place of residence had statistically significant effect on anxiety, and gender had statistically significant effect on stress. Conclusion The study confirmed an alarming number of nursing students who experienced anxiety, stress, and depression. This study serves as an evidence concerning nursing students’ mental health issues as a consequence of the COVID-19 pandemic.