Introduction and aims The demographic and clinical profile and dynamics of real-time polymerase chain reaction (RT-PCR) in coronavirus disease 2019 (COVID-19) patients are not well understood. The study aimed to analyze the demographic, clinical, and RT-PCR profiles of COVID-19 patients. Methodology The study was a retrospective, observational study conducted at a COVID-19 care facility, and the study period was from April 2020 to March 2021. Patients with laboratory-confirmed COVID-19 by real-time polymerase chain reaction (RT-PCR) were enrolled in the study. Patients with incomplete details or with only single PCR tests were excluded. Demographic and clinical details and the results of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) RT-PCR collected at different time points were retrieved from the records. The statistical software Minitab version 17.1.0 package (Minitab, LLC, State College, PA, USA) and Rstudio version 1.3.959 (Rstudio, Boston, MA, USA) were used for the statistical analysis. Results The mean duration from symptom onset to the last positive RT-PCR was 14.2 ± 4.2 days. The proportions of positive RT-PCR tests were 100%, 40.6%, 7.5%, and 0% at the end of the first, second, third, and fourth weeks of illness. The median duration of days to first negative RT-PCR in the asymptomatic patients was 8 ± 4 days, and 88.2% of asymptomatic patients were RT-PCR-negative within 14 days. A total of 16 symptomatic patients had prolonged positive test results even after three weeks of symptom onset. Older patients were associated with prolonged RT-PCR positivity. Conclusion This study revealed that the average period of RT-PCR positivity from the onset of symptoms is >2 weeks in symptomatic COVID-19 patients. Prolonged observation in the elderly population and repeat RT-PCR before discharge or discontinuation of quarantine is required.