COVID-19 is a challenge for education systems around the world. This study aimed to evaluate the perceived impact of the COVID-19 pandemic on nursing students, by assessing their emotions, the level of concern in contracting the virus and their perceived stress. We conducted an observational cross-sectional study. A total of 709 nursing students completed an anonymous questionnaire. The levels of anxiety and stress were assessed using the generalized anxiety disorder scale and the COVID-19 student stress questionnaire, respectively. In total, 56.8% of the sample often or always found it difficult to attend distance-learning activities. The main difficulty referred to was connection problems (75.7%). The mean generalized anxiety disorder score was 9.46 (SD = 5.4) and appeared almost homogeneous among students across the three years of study; most of the students showed mild (35%) to moderate (27%) levels of anxiety; 19% had severe anxiety. The overall COVID-19 stressor mean scores were 11.40 (SD = 6.50); the majority of the students (47.1%) showed scores indicative of moderate stress, 25% showed low stress levels, and 28% showed high-stress levels. Improvements and investments are needed to ensure high-quality distance learning, adequate connectivity, technical support for students, as well as strategies to promote mental health.