Introduction: The COVID-19 pandemic has significantly impacted stress levels across various professions, particularly in the medical field. This increase in stress has also affected medical students, including nursing students, who faced unprecedented and challenging circumstances. Nursing students, in particular, experienced added pressure due to observing the frontline experiences of nurses and the new demands placed upon them. Aim: This study aimed to assess whether the COVID-19 pandemic affected an increase in stress levels among nursing students in Poland during the pandemic. We also attempt to determine whether there is a correlation between the stress level of students and factors such as gender, age, place of residence, marital status, and level of education. Assuming that the stress level will be higher among women of increasing age and bachelor’s students, we also assumed, however, that lower stress levels would occur among people in relationships and living in the countryside. Materials and Methods: The study was conducted from 27 April 2022 to 12 May 2022. We chose that period as it was the final one of the COVID-19 pandemic, and there was an increasing amount of discussion concerning its cessation, with the public accustomed to its presence in our everyday lives. Since we wanted to determine the stress level experienced by students, we decided to use the standardized Perceived Stress Scale (PSS-10). We enriched the study with sociodemographic questions to investigate the potential impact of these characteristics on the degree of stress experienced. Results: The average score obtained by respondents on the PSS-10 was 19.57 ± 6.03. Of the respondents, 49% reported experiencing a high level of stress. No statistically significant differences were found between the mean PSS-10 scores and the gender (Z = 0.169; p = 0.865), age (F = 1.282, p = 0.281), marital status (Z = −0.776, p = 0.437), or place of residence (urban vs. rural) (Z = −0.784, p = 0.433) of the respondents. The mean PSS-10 scores were also analyzed regarding the level of education (bachelor’s vs. master’s). Bachelor’s students had an average PSS-10 score of 18.95 ± 6.42, while master’s students scored 20.05 ± 5.70. Again, no statistically significant differences were found (t = −1.102, p = 0.2720). Conclusions: The study indicated that nursing students experience high stress levels regardless of gender, age, marital status, place of residence, or level of education. High stress levels were reported among both bachelor’s and master’s students. Keywords: stress; COVID-19 pandemic; students nursing