COVID-19 has been considered a possible cause of post-traumatic stress disorder (PTSD) or similar conditions. However, what specific disease symptoms may contribute most to prolonged PTSD-like symptoms in COVID-19 survivors is unclear. The study aimed to present the factor structure of COVID-19 symptoms and identify which symptoms of COVID-19 best explain the subsequent presence of PTSD-like symptoms in mild COVID-19 survivors. COVID-positive adults (n = 341) completed online self-report scales at the baseline assessment (T1) and after approximately 4 months (T2), including The Patient Health Questionnaire Anxiety-Depression Scale; The Scale of Psychosocial Experience Related to COVID-19, The Primary Care PTSD Screen for DSM-5; and self-designed questionnaires evaluating the severity of COVID-related medical and neurocognitive symptoms and pre-pandemic variables. Exploratory factor analysis revealed five factors of COVID-19 symptoms: flu-like, respiratory, cold, neurological, and neurocognitive. Hierarchical logistic regression showed that besides selected control variables (anxiety and depression, presence of PTSD-like symptoms, COVID-related stigma in T1), neurocognitive symptoms of COVID-19 in T1 but not other symptoms of the disease were a significant predictor of the presence of PTSD-like symptom in T2. Findings suggest a need for a comprehensive neurocognitive assessment of people diagnosed with COVID-19 and prompt interventions targeting the prevention of potential risks for long-term PTSD-like states at the community level.