Studies of metal accumulation in fish are mainly focused on the muscle tissue, while the metal accumulation patterns in other tissues have been largely neglected. Muscle is not always a good indicator of the whole fish body contamination. Elemental accumulation in many fish tissues and organs and their potential use in monitoring programs have not received proper attention. In the present study, As, Cd, Co, Cr, Cu, Fe, Hg, Mn, Ni, Pb, Se, and Zn concentrations were assessed by inductively coupled plasma mass spectrometry (ICP-MS) in the following 14 tissues of the wels catfish (Silurus glanis) from the Danube River: muscle, gills, spleen, liver, kidneys, intestine, gizzard, heart, brain, gallbladder, swim bladder, vertebra, operculum, and gonads. A high level of differential elemental accumulation among the studied tissues was observed. The maximum overall metal accumulation was observed in the vertebra, followed by the kidneys and liver, with the metal pollution index (MPI) values of 0.26, 0.25, and 0.24, respectively. The minimum values were observed in the gallbladder, muscle, brain, and swim bladder, with MPI values of 0.03, 0.06, 0.07, and 0.09, respectively. Average metal concentrations in the fish muscle were below the maximum allowed concentrations for human consumption. The mean As, Cd, Pb, Cu, Fe, and Zn concentrations in the muscle were 0.028, 0.001, 0.001, 0.192, 3.966, and 3.969 μg/g wet weight, respectively. We believe that the presented findings could be of interest for the scientific community and freshwater ecosystem managers. There is a need for further research that would assess less studied tissues in different fish species.