This paper analyzes the groundwater in the deep Quaternary aquifer of Eastern Croatia. These waters are collected at the Vinogradi Pumping Station (Osijek, Croatia) for the needs of public water supply. This research aimed to assess the impact of climate extremes, namely, high air temperatures and low rainfall, on the quantity and quality of groundwater. On the basis of data from the Vinogradi Pumping Station in the period 1987–2015, three extremely warm and low-water years were singled out. For these three years, the following were analyzed: climate diagrams, groundwater levels (in the piezometers closest to and farthest from the pumping station), and the quality of the affected groundwater. The results of this research indicate that the reaction of aquifers to the analyzed extreme climatic conditions for the observed period was manifested in the variation of the amplitude of groundwater levels by a maximum of 4–5 m. Considering the total thickness of the affected layers (60–80 m), this variation is not a concern from the point of view of water supply. As for the quality of groundwater, it was found to be of constant quality in its composition and was not affected by climatic extremes.