Introduction: Working during the COVID-19 pandemic is a particular challenge for nurses because, while performing their daily routines, they are exposed to physical and social consequences of the SARS-CoV-2 virus, which is accompanied by intensified stress. The aim of this study was to assess the intensity of stress and coping strategies applied by nurses working with both infected and non-infected patients with SARS-CoV-2 virus during the COVID-19 pandemic. Materials and Methods: The study was conducted between January and March 2021. Due to the epidemiological situation, the questionnaire was posted on Facebook in nurses’ groups and sent out via the “Messenger” and “WhatsApp” applications. Stress intensity was assessed by means of the Perceived Stress Scale (PSS-10), whereas coping strategies were assessed using the Mini-COPE stress coping inventory. Results: Among 151 surveyed nurses, more than half (52.3%) worked with infected patients and the remaining ones (47.7%) worked with non-infected patients. The level of stress perceived by nurses working with infected patients was higher than among nurses working with patients without SARS-CoV-2 infection (22.22 ± 5.94 vs. 20.21 ± 5.68, p = 0.03). The nurses working with infected patients were most likely to choose coping strategies focused on the problem (2.00 ± 0.62) and emotions (2.01 ± 0.69), whereas those working with non-infected patients usually chose strategies focused only on the problem (2.11 ± 0.58). Conclusions: During the COVID-19 pandemic, nurses working with SARS-CoV-2 patients experienced more intense stress than those working with non-infected patients. Nurses working with SARS-CoV-2 patients tended to cope with stress using strategies focused on the problem and on emotions, while those working with non-infected patients were more likely to choose strategies focused only on the problem.