Background: The coronavirus disease (COVID-19) emerged from China and rapidly spread to many other countries. In this study, we investigated the prevalence of post-traumatic stress disorder (PTSD) among patients with COVID-19 who were treated and discharged from a university hospital in Daegu, Korea. Methods: In total, 64 patients who were diagnosed with COVID-19 and then hospitalized, treated and discharged from the university hospital between February and April 2020 participated in our study. We conducted telephone interviews with the participants and evaluated the presence of PTSD using the Post-Traumatic Stress Disorder Checklist-5 (PCL-5) based on the Diagnostic and Statistical Manual of Mental Disorders (DSM-5; score range: 0–80). If a score of ≥33 was obtained, then a diagnosis of PTSD was made. We analyzed the association between PTSD and demographic and clinical characteristics using the Mann–Whitney U and chi-square tests. Results: In total, 13 patients had a PCL-5 score of ≥33, which indicated that 20.3% (n = 64) of the patients had PTSD. No significant differences were observed in demographic characteristics, including, sex, age, hospitalization time and duration after discharge, between patients with PTSD and those without PTSD. Conclusions: The prevalence rate of PTSD was 20.3% in patients with COVID-19 who had been hospitalized, treated and discharged. Accordingly, clinicians should be aware of the high possibility of PTSD among COVID-19 patients. Mental health interventions supporting the mental health of patients should be provided to affected patients.