Water scarcity in arid regions is exacerbated by water quality degradation from anthropogenic contamination. In water-scarce regions, it is crucial to identify hydrochemical characteristics and pollution sources for effective water resource management. In this study, the Hei River—located in the Loess Plateau of China, which is an arid region with substantial anthropogenic-induced environmental changes—was selected as the study area to investigate these issues. The major ions of 242 streamflow and groundwater samples were measured during the 2014 and 2015 dry and flood seasons. Using a Piper diagram, a fuzzy membership function, a Gibbs diagram, and a forward model, the hydrochemical facies and water quality of streamflow and groundwater were investigated, and the main river solute sources and relative contributions were determined using quantitative and qualitative methods. The total dissolved solids were 279.6 ± 127.8 mg·L−1 for streamflow and 354.0 ± 157.4 mg·L−1 for groundwater, indicating low salinity water. However, the hydrochemical characteristics varied with season and location. Qualitatively, the atmospheric inputs, human activities, and rock weathering all contributed solutes to the waters but with varying contributions. The following are the mean contributions of analyzed solute source: silicate weathering (45.1 ± 1.1%) > carbonate weathering (34.1 ± 1.6%) > evaporite dissolution (13.7 ± 2.4%) > atmospheric input (5.4 ± 0.1%) > anthropogenic input (1.7 ± 0.1%). In general, water quality was satisfactory, as the majority of samples conformed to drinking water standards. The samples had good water quality because the river solutes were not heavily affected by anthropogenic activities and were primarily controlled by rock weathering. However, localized areas of high anthropogenic impact were identified. Such locations should be prioritized for pollution control and water resource management.