Background: Respiratory syncytial virus (RSV) is an important cause of childhood hospitalizations. The aim of the study was to estimate the rates of RSV-related hospitalizations in children aged less than 5 years in Poland. Methods: This retrospective observational cohort study was based on data obtained from the National Health Fund in Poland regarding all acute respiratory tract infections and RSV-coded admissions of children (age <5 years) to public hospitals between July 2015 and June 2023. Patients were stratified based on the following age groups: 0–1 month, 2–3 months, 4–6 months, 7–12 months, 13–24 months, and 25–60 months. Results: The number of RSV-related hospitalizations increased every season, both before and through the ending phase of the coronavirus disease 2019 (COVID-19) pandemic. The COVID-19 pandemic was associated with a shift in the seasonality pattern of RSV infection. Hospitalization rates per 1000 inhabitants were the highest for children aged 0–12 months, reaching 47.3 in the 2022/23 season. Within this group, the highest hospitalization rate was observed for children aged 2–3 months—94.9 in the 2022/23 season. During the ending phase of the COVID-19 pandemic, the observed increase in admission rates was 2-, 4-, and 5-fold the pre-COVID rate for children aged <12 months, 12–24 months, and 25–60 months, respectively. Conclusions: In Poland, RSV infections cause a significant burden in hospitalized children aged less than 5 years. RSV-related hospitalizations were most frequent in children aged less than 1 year. The COVID-19 pandemic was associated with a shift in the seasonality pattern of RSV infections. After the pandemic, more RSV-related hospitalizations were observed in older children (aged 13 months and older) vs. the pre-pandemic phase.