Minimizing human exposure to arsenic (As) and ensuring an adequate dietary intake of selenium (Se) are significant issues in research on food sources. This study measured the content of As and Se in the muscles, gills, liver, and gonads of the fish round goby (Neogobius melanostomus) to assess the benefits and risks associated with their consumption. This was achieved by using dietary reference intake (DRI), estimated daily intake (EDI), target hazard quotient (THQ), and carcinogenic risk (CR). The elements were analyzed by atomic absorption spectrometry. The mean concentrations of As and Se (in μg kg−1 wet weight) were 25.1 and 161.4 in muscle, 58.8 and 367.4 in liver, 47.4 and 635.3 in gonads, and 16.4 and 228.5 in gills, respectively. Arsenic in the muscle portion of fish accounted for up to 0.5% of the DRI, while Se constituted approximately 30% of the DRI. The EDI values were below the reference oral dose (RfD). The THQ were much below the permissible levels (THQ < 1), and the CR were at least within the permissible limit (CR < 10−4). With regard to the As content, round goby muscles can be deemed safe for consumers. They may also be a valuable source of Se in the human diet. However, round goby consumption should be monitored for the proper and safe intake of these elements.