Objective To estimate the economic burden of non‐communicable diseases (NCDs) in people living with HIV (PLWH) in Denmark. Methods We conducted a cohort study using population‐based Danish medical registries including all adult residents of the Central Denmark Region registered with a first‐time HIV‐diagnosis during the period 2006–2017. For each PLWH, we matched 10 persons without HIV from the background population by birth year, sex and municipality of residence. Information on healthcare utilization and costs for the PLWH and non‐HIV cohorts was retrieved from register data. For each cohort, we estimated the annual costs for major disease categories (HIV care, other somatic care, and psychiatric care) in the period from 3 years before to 9 years after diagnosis/matching date. Results We identified 407 PLWH and 4070 persons from the background population. The total healthcare costs during the study period were approximately three times higher for PLWH compared to the non‐HIV cohort (€76 198 vs. €23 692). Average annual cost of hospital care, primary care and selected prescription medicine was estimated to be €6987 per year in the years after the diagnosis compared to €2083 per year in the non‐HIV cohort. In PLWH, the cost of NCDs and psychiatric care was approximately two times higher than the cost of HIV care. Conclusion PLWH have higher healthcare costs stemming from three areas: excess cost due to the HIV infection, the treatment of NCDs, and psychiatric care.