The karst aquifer of the Ljubljanica River catchment, which has numerous springs and sinks, presents an interesting environment for studying hydrogeological processes. This study aims to explore the behavior of U isotopes and to evaluate their use as tracers of hydrogeochemical processes as an alternative to classical geochemical tracers (i.e., physicochemical parameters, elemental ratios, and alkalinity) involved in water–rock interactions and water flow in this karst water system. Basic hydrochemical parameters, as well as the spatiotemporal variations of total U concentrations, $^{234}$U/$^{238}$U activity ratios, and δ $^{238}$U values, were monitored in water samples from springs and sinks under different hydrological conditions. The bedrock as the source of dissolved and detrital U was also analyzed. Multi-collector inductively couple plasma-mass spectrometry results reveal variations of the $^{234}$U/$^{238}$U activity ratios, which are consistently negatively correlated with the discharge at most analyzed sites. Large $^{238}$U/$^{235}$U isotope fractionation occurred during bedrock weathering, and the large variability of the measured δ$^{238}$U values is seemingly unrelated to the lithological characteristics of the bedrock or discharge. Our results confirm that $^{234}$U/$^{238}$U activity ratios in water can be used as a tracer for studying changes in groundwater flows and the mixing of waters of different origins under different hydrological conditions.