Abstract Background Population-level knowledge on individuals at high risk of severe and fatal coronavirus disease 2019 (COVID-19) is urgently needed to inform targeted protection strategies in the general population. Methods We examined characteristics and predictors of hospitalization and death in a nationwide cohort of all Danish individuals tested for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) from 27 February 2020 until 19 May 2020. Results We identified 11 122 SARS-CoV-2 polymerase chain reaction-positive cases of whom 80% were community-managed and 20% were hospitalized. Thirty-day all-cause mortality was 5.2%. Age was strongly associated with fatal disease {odds ratio [OR] 15 [95% confidence interval (CI): 9–26] for 70–79 years, increasing to OR 90 (95% CI: 50–162) for ≥90 years, when compared with cases aged 50–59 years and adjusted for sex and number of co-morbidities}. Similarly, the number of co-morbidities was associated with fatal disease [OR 5.2 (95% CI: 3.4–8.0), for cases with at least four co-morbidities vs no co-morbidities] and 79% of fatal cases had at least two co-morbidities. Most major chronic diseases were associated with hospitalization, with ORs ranging from 1.3–1.4 (e.g. stroke, ischaemic heart disease) to 2.6–3.4 (e.g. heart failure, hospital-diagnosed kidney disease, organ transplantation) and with mortality with ORs ranging from 1.1–1.3 (e.g. ischaemic heart disease, hypertension) to 2.5–3.2 (e.g. major psychiatric disorder, organ transplantation). In the absence of co-morbidities, mortality was <5% in persons aged ≤80 years. Conclusions In this nationwide population-based COVID-19 study, increasing age and multimorbidity were strongly associated with hospitalization and death. In the absence of co-morbidities, the mortality was, however, <5% until the age of 80 years.