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The aim of this study is to determine the main variables associated with nurses’ sickness absence (SA) and to improve the prediction of SA based on pandemic-related experiences. The second aim is to examine the differences between COVID-19 (CoV) and non-COVID-19 (non-CoV) nurses in levels of post-traumatic stress disorder (PTSD) symptoms, personality traits, coping strategies and professional stressors experienced. This historical prospective study enrolled 1305 nurses from the University Hospital of Split, Croatia. A total of 380 subjects participated in the study, 163 non-CoV and 217 CoV subjects. Nurses’ pandemic-related experience questionnaires, Big Five Inventory (BFI), Post-traumatic Stress Disorder Checklist (PCL-5), Coping Inventory for Stressful Situations (CISS) and Occupational Stress Questionnaire, were used for evaluation. Non-CoV nurses felt more fear of infection, were more socially distanced, had more PTSD symptoms and neuroticism and felt more stress due to public criticism and job requirements compared to CoV nurses; p < 0.001. The groups of SA users and non-SA users could be distinguished based on predictor variables in CoV and non-CoV nurses, with a correct classification of 84.8% vs. 79.1%. It was possible to predict the probability of using SA among nurses due to pandemic professional experience, personality traits and coping strategies.