The climatic changes observed in Poland are manifested by an increase in air temperature, but not an increase in rainfall, which causes an increase in the water needs of plants, and hence the necessity to develop irrigation systems for crops. The aim of this study was to assess the water needs of grapevines in 2021–2050 in the Bydgoszcz region (northern Poland), an area with high requirements for supplementary irrigation. The calculations were based on the expected changes in air temperature according to the climate change scenario for Poland: the 4th Intergovernmental Panel on Climate Change—Special Report on Emissions Scenarios: balanced scenario (A1B). The average monthly temperature in 1981–2010 was used in the calculations. The water needs of grapevines were estimated using the reference evapotranspiration calculated using the Blaney–Criddle equation, and then using the crop coefficient and potential (crop) evapotranspiration. It was found that in 2021–2050, the water needs of grapevines, both during the growing season (May–September) and during the irrigation period (June–August), will increase by 6%. The highest and significant increase in water needs, by 10%, should be expected in August. The estimated increase in water needs of grapevines indicates the need to development sustainable irrigation systems for vineyards in northern Poland.