Background: Health-care workers are thought to be highly exposed to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection. We aimed to investigate the prevalence of antibodies against SARS-CoV-2 in health-care workers and the proportion of seroconverted health-care workers with previous symptoms of COVID-19. Methods: In this observational cohort study, screening was offered to health-care workers in the Capital Region of Denmark, including medical, nursing, and other students who were associated with hospitals in the region. Screening included point-of-care tests for IgM and IgG antibodies against SARS-CoV-2. Test results and participant characteristics were recorded. Results were compared with findings in blood donors in the Capital Region in the study period. Findings: Between April 15 and April 23, 2020, we screened 29 295 health-care workers, of whom 28 792 (98·28%) provided their test results. We identified 1163 (4·04% [95% CI 3·82–4·27]) seropositive health-care workers. Seroprevalence was higher in health-care workers than in blood donors (142 [3·04%] of 4672; risk ratio [RR] 1·33 [95% CI 1·12–1·58]; p<0·001). Seroprevalence was higher in male health-care workers (331 [5·45%] of 6077) than in female health-care workers (832 [3·66%] of 22 715; RR 1·49 [1·31–1·68]; p<0·001). Frontline health-care workers working in hospitals had a significantly higher seroprevalence (779 [4·55%] of 16 356) than health-care workers in other settings (384 [3·29%] of 11 657; RR 1·38 [1·22–1·56]; p<0·001). Health-care workers working on dedicated COVID-19 wards (95 [7·19%] of 1321) had a significantly higher seroprevalence than other frontline health-care workers working in hospitals (696 [4·35%] of 15 983; RR 1·65 [1·34–2·03]; p<0·001). 622 [53·5%] of 1163 seropositive participants reported symptoms attributable to SARS-CoV-2. Loss of taste or smell was the symptom that was most strongly associated with seropositivity (377 [32·39%] of 1164 participants with this symptom were seropositive vs 786 [2·84%] of 27 628 without this symptom; RR 11·38 [10·22–12·68]). The study is registered at ClinicalTrials.gov, NCT04346186. Interpretation: The prevalence of health-care workers with antibodies against SARS-CoV-2 was low but higher than in blood donors. The risk of SARS-CoV-2 infection in health-care workers was related to exposure to infected patients. More than half of seropositive health-care workers reported symptoms attributable to COVID-19. Funding: Lundbeck Foundation.