Background It remains unclear whether COVID-19 is associated with psychiatric symptoms during or after the acute illness phase. Being affected by the disease exposes the individual to an uncertain prognosis and a state of quarantine. These factors can predispose individuals to the development of mental symptoms during or after the acute phase of the disease. There is a need for prospective studies assessing psychiatric symptoms in COVID-19 patients in the post-infection period. Methods In this prospective cohort study, nasopharyngeal swabs for COVID-19 tests were collected at patients' homes under the supervision of trained healthcare personnel. Patients who tested positive for COVID-19 and were classified as mild cases (N = 895) at treatment intake were further assessed for the presence of psychiatric symptoms (on average, 56.6 days after the intake). We investigated the association between the number of COVID-19 symptoms at intake and depressive, anxiety and post-traumatic symptoms approximately two months later, adjusting for previous mental health status, time between baseline and outcome, and other confounders. Multivariate logistic regression and generalized linear models were employed for categorical and continuous outcomes, respectively. Results A clinically significant level of depressive, anxiety and post-traumatic stress symptoms were reported by 26.2% (N = 235), 22.4% (N = 201), and 17.3% (N = 155) of the sample. Reporting an increased number of COVID-related symptoms was associated with the presence of clinically significant levels of depressive (aOR = 1.059;95%CI = 1.002–1.119), anxiety (aOR = 1.072;95%CI = 1.012–1.134), and post-traumatic stress (aOR = 1.092;95%CI = 1.024–1.166) symptoms. Sensitivity analyses supported findings for both continuous and categorical measures. Conclusion Exposure to an increased number of COVID-19 symptoms may be associated with depressive, anxiety and post-traumatic symptoms after the acute phase of the disease. These patients should be monitored for the development of psychiatric symptoms after COVID-19 treatment discharge. Early interventions, such as brief interventions of psychoeducation on coping strategies, could benefit these individuals.