Reports of persistent symptoms after hospitalization with COVID-19 have raised concern of a "long COVID" syndrome. This study aimed at determining the prevalence of and risk factors for acute and persistent symptoms in non-hospitalized patients with polymerase chain reaction (PCR) confirmed COVID-19. We conducted a cohort study of non-hospitalized participants identified via the Danish Civil Registration System with a SARS-CoV-2-positive PCR-test and available biobank samples. Participants received a digital questionnaire on demographics and COVID-19-related symptoms. Persistent symptoms: symptoms > 4 weeks (in sensitivity analyses > 12 weeks). We included 445 participants, of whom 34% were asymptomatic. Most common acute symptoms were fatigue, headache, and sneezing, while fatigue and reduced smell and taste were most severe. Persistent symptoms, most commonly fatigue and memory and concentration difficulties, were reported by 36% of 198 symptomatic participants with follow-up > 4 weeks. Risk factors for persistent symptoms included female sex (women 44% vs. men 24%, odds ratio 2.7, 95% CI 1.4-5.1, p = 0.003) and BMI (odds ratio 1.1, 95% CI 1.0-1.2, p = 0.001). In conclusion, among non-hospitalized PCR-confirmed COVID-19 patients one third were asymptomatic while one third of symptomatic participants had persistent symptoms illustrating the heterogeneity of disease presentation. These findings should be considered in health care planning and policy making related to COVID-19.