The Yarlung Zangbo River (YZR) is the longest plateau river in China and has famous tributaries, the Lhasa River and the Nianchu River. A total of 75 water samples were collected from the Yarlung Zangbo River Basin (YZRB) in this study to investigate the dissolved concentration, spatial distribution, and source of trace elements (Fe, V, Be, Ti, Mo, Se, Cd, Zn, Cu, Ni, Co, Mn, Cr, Ba, Tl, Pb, Hg, As, and Sb). The results indicate that only Cr and Tl contaminate water, while the other trace elements were in an unpolluted state. In addition, correlation analysis showed that there was a highly significant positive correlation between the concentrations of As, Sb, and Mo; there was also a highly significant positive correlation between the concentrations of Fe, Mn, Ti, Pb, Ni, Co, and Ba. The results of Positive Matrix Factorization (PMF) showed that there were four sources of trace elements in the YZRB, including the resuspension and dissolution of sediments (16.283%), agricultural source (11.436%), lithological source (47.418%), and soil-forming rocks (6.374%). Cluster analysis combined with PMF normalized contribution analysis, which showed that the trace elements found in the YZR’s mainstream were predominantly influenced by the surrounding rocks composition. Meanwhile, both the discharge of mining wastewater and sediments were marked in the Lhasa River. Additionally, agricultural activities were the chief contributors to the trace elements in the Nianchu River. Furthermore, the entire basin was subjected to the influence of soil-forming rocks. This study comprehensively analyzed and evaluated the physicochemical properties of water, the spatial distribution, and the pollution degree, and performed source analysis of trace elements in the YZRB. This research provides a foundational reference for further investigation of the spatial distribution and origins of trace elements in the rivers of the Qinghai–Tibet Plateau (QTP).