Respiratory syncytial virus (RSV) is a major cause of hospitalisation in infants. The burden of RSV infection in healthy term infants has not yet been established. Accurate health-care burden data in healthy infants are necessary to determine RSV immunisation policy when RSV immunisation becomes available. We performed a multicentre, prospective, observational birth cohort study in healthy term-born infants (≥37 weeks of gestation) in five sites located in different European countries to determine the health-care burden of RSV. The incidence of RSV-associated hospitalisations in the first year of life was determined by parental questionnaires and hospital chart reviews. We performed active RSV surveillance in a nested cohort to determine the incidence of medically attended RSV infections. The study is registered with ClinicalTrials.gov, NCT03627572. In total, 9154 infants born between July 1, 2017, and April 1, 2020, were followed up during the first year of life and 993 participated in the nested active surveillance cohort. The incidence of RSV-associated hospitalisations in the total cohort was 1·8% (95% CI 1·6-2·1). There were eight paediatric intensive care unit admissions, corresponding to 5·5% of 145 RSV-associated hospitalisations and 0·09% of the total cohort. Incidence of RSV infection in the active surveillance cohort confirmed by any diagnostic assay was 26·2% (24·0-28·6) and that of medically attended RSV infection was 14·1% (12·3-16·0). RSV-associated acute respiratory infection causes substantial morbidity, leading to the hospitalisation of one in every 56 healthy term-born infants in high-income settings. Immunisation of pregnant women or healthy term-born infants during their first winter season could have a major effect on the health-care burden caused by RSV infections. Innovative Medicines Initiative 2 Joint Undertaking, with support from the EU's Horizon 2020 research and innovation programme and European Federation of Pharmaceutical Industries and Associations.