In this work, the capacity of the Fenton oxidation process for the degradation of color and organic matter contained in the wastewater generated in the leather dyeing stage (WWDS) of an industrial tannery was evaluated. The wastewater characteristics included, among others, high toxicity (lethal concentration for Artemia salina, 24 h test, 50% of population = 93.71 ppm), high dye concentration (36 mg/L, yellow color), high chromium concentration (3.34 mg/L), and low biodegradability index (BOD5/COD ratio = 0.083). From an experimental design, the response surface methodology, and the multiobjective optimization analysis, the following optimal operating conditions were established: initial pH = 3.15, [Fe2+] = 0.981 mM, and [H2O2] = 5.38 mM. After 10 min of oxidation (determined from kinetic studies), it reached approximately 97% decolorization, COD reduction of approximately 82%, and TOC mineralization of approximately 92%. A synergistic effect of Fenton’s reagents for TOC removal (STOC = 0.8) and decolorization (SCN = 0.28) of the WWDS under study was confirmed experimentally. An increase in the biodegradability index, to a value of approximately 0.3, was confirmed. The cost of the treatment was estimated at 0.0112 USD/m3. Thus, the Fenton oxidation process allowed compliance with current Colombian environmental regulations and considerably improved the biodegradability and toxicity characteristics of the studied industrial effluent. It can be considered as an efficient alternative, easy to carry out on an industrial batch scale, and economically viable for the treatment of wastewater from the leather dyeing stage of an industrial tannery.