Objectives: To investigate the prevalence and burden of proxy-reported acute symptoms in children in the first 4 weeks after detection of severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) infection, and factors associated with symptom burden. Methods: Nationwide cross-sectional survey using parental proxy reporting of symptoms associated with SARS-CoV-2 infection. In July 2021, a survey was sent to the mothers of all Danish children aged 0–14 years with a positive SARS-CoV-2 polymerase chain reaction (PCR) test between January 2020 and July 2021. The survey included 17 symptoms associated with acute SARS-CoV-2 infection and questions about comorbidities. Results: Of 38,152 children with a positive SARS-CoV-2 PCR test, 10,994 (28.8%) mothers responded. The median age was 10.2 (range 0.2–16.0) years and 51.8% were male. Among participants, 54.2% (n=5957) reported no symptoms, 43.7% (n=4807) reported mild symptoms, and 2.1% (n=230) reported severe symptoms. The most common symptoms were fever (25.0%), headache (22.5%) and sore throat (18.4%). Asthma {odds ratio (OR) 1.91 [95% confidence interval (CI) 1.57–2.32) and OR 2.11 (95% CI 1.36–3.28)}, allergy [OR 1.31 (95% CI 1.14–1.52) and OR 1.70 (95% CI 1.18–2.46], eczema [OR 1.43 (95% CI 1.20–1.71) and OR 2.03 (95% CI 1.38–2.97)] and OCD/anxiety/depression [OR 2.06 (95% CI 1.39–3.06) and OR 3.79 (95% CI 1.80–7.97)] were associated with reporting a higher symptom burden [values indicate outcomes reporting three or more acute symptoms (upper quartile) and reporting a severe symptom burden, respectively]. The highest prevalence of symptoms was found among children aged 0–2 and 12–14 years. Conclusions: Among SARS-CoV-2-positive children aged 0–14 years, approximately half reported no acute symptoms within the first 4 weeks after a positive PCR test. Most symptomatic children reported mild symptoms. Several comorbidities were associated with reporting a higher symptom burden.