In dense urban areas, trees are often planted in small root spaces. This results in an insufficient water supply in droughts, affecting the trees’ vitality and evapotranspiration performance. However, water availability can be improved by irrigation. The study investigated whether weekly manual or daily irrigation through a rainwater harvesting system (RHS) fed by connected impermeable surfaces is sufficient to avoid drought stress. Using a 12 m³ root volume of the German minimum planting standard, we implemented a daily urban tree water balance model in a moderate climate, considering the future and current climate. We analyzed the site conditions for a 60-year-old tree in five cities in southern Germany. The results showed that weekly irrigation, as carried out in practice, does not prevent drought stress or significantly reduce drought duration compared to a tree without irrigation in all investigated locations. However, the application of daily irrigation with stormwater from an RHS reduces the duration of droughts, as shown for the species Platanus x acerifolia, which has a comparably high water demand. We optimized the required RHS storage volume depending on the tree species and location, as climate significantly influences water demand and supply. According to our results, future climate conditions must be considered in planning, as larger RHS storage volumes may be required.