Background: Estimates of the severity of the SARS-CoV-2 omicron variant (B.1.1.529) are crucial to assess the public health impact associated with its rapid global dissemination. We estimated the risk of SARS-CoV-2-related hospitalisations after infection with omicron compared with the delta variant (B.1.617.2) in Denmark, a country with high mRNA vaccination coverage and extensive free-of-charge PCR testing capacity. Methods: In this observational cohort study, we included all RT-PCR-confirmed cases of SARS-CoV-2 infection in Denmark, with samples taken between Nov 21 (date of first omicron-positive sample) and Dec 19, 2021. Individuals were identified in the national COVID-19 surveillance system database, which included results of a variant-specific RT-PCR that detected omicron cases, and data on SARS-CoV-2-related hospitalisations (primary outcome of the study). We calculated the risk ratio (RR) of hospitalisation after infection with omicron compared with delta, overall and stratified by vaccination status, in a Poisson regression model with robust SEs, adjusted a priori for reinfection status, sex, age, region, comorbidities, and time period. Findings: Between Nov 21 and Dec 19, 2021, among the 188 980 individuals with SARS-CoV-2 infection, 38 669 (20·5%) had the omicron variant. SARS-CoV-2-related hospitalisations and omicron cases increased during the study period. Overall, 124 313 (65·8%) of 188 980 individuals were vaccinated, and vaccination was associated with a lower risk of hospitalisation (adjusted RR 0·24, 95% CI 0·22–0·26) compared with cases with no doses or only one dose of vaccine. Compared with delta infection, omicron infection was associated with an adjusted RR of hospitalisation of 0·64 (95% CI 0·56–0·75; 222 [0·6%] of 38 669 omicron cases admitted to hospital vs 2213 [1·5%] of 150 311 delta cases). For a similar comparison by vaccination status, the RR of hospitalisation was 0·57 (0·44–0·75) among cases with no or only one dose of vaccine, 0·71 (0·60–0·86) among those who received two doses, and 0·50 (0·32–0·76) among those who received three doses. Interpretation: We found a significantly lower risk of hospitalisation with omicron infection compared with delta infection among both vaccinated and unvaccinated individuals, suggesting an inherent reduced severity of omicron. Our results could guide modelling of the effect of the ongoing global omicron wave and thus health-care system preparedness. Funding: None.