The consumption of functional foods and nutraceuticals is gaining more importance in modern society. The exploration of alternative sources and the utilization of by-products coming from the food industry are gaining more importance. The present study aimed to characterize the nutritional value and potential use of sea bass by-products as a source of high-added-value compounds for the development of supplements. The chemical composition (moisture, protein, fat, and ash contents) and profiles of amino acids (high-performance liquid chromatography coupled to a scanning fluorescence detector), fatty acids (gas chromatography coupled to a flame ionization detector), and minerals (inductively coupled plasma optical emission spectroscopy) were determined for sea bass fillet and its by-products (skin, guts, gills, liver, head, and fish bones). The chemical composition assays revealed that by-products were rich sources of proteins (skin; 25.27 g/100 g), fat (guts and liver; 53.12 and 37.25 g/100 g, respectively), and minerals (gills, head, and fish bones; 5.81, 10.11, and 7.51 g/100 g, respectively). Regarding the amino-acid profile, the skin and liver were the main sources of essential amino acids with an essential amino-acid index of 208.22 and 208.07, respectively. In the case of the fatty-acid profile, all by-products displayed high amounts of unsaturated fatty acids, particularly monounsaturated (from 43.46 to 49.33 g/100 g fatty acids) and omega-3 fatty acids (in the range 10.85–14.10 g/100 g fatty acids). Finally, the evaluation of mineral profile indicated high contents of calcium and phosphorus in gills (1382.62 and 742.60 mg/100 g, respectively), head (2507.15 and 1277.01 mg/100 g, respectively), and fish bone (2093.26 and 1166.36 mg/100 g, respectively). Therefore, the main sources of monounsaturated, unsaturated, and long-chain omega-3 fatty acids were guts and liver. The most relevant source of minerals, particularly calcium, phosphorus, and manganese, were head, fish bones, and gills. The most promising source of proteins and amino acids was the skin of sea bass.