Bauxite residue (BR) is a by-product of bauxite refining using Bayer process for alumina production, which contains numerous valuable components: iron (Fe), aluminum (Al), and rare earth elements such as scandium (Sc). The main issue of previous research for the Sc extraction from BR was the low extraction efficiency or high Fe co-extraction. This article shows that Fe co-extraction can be significantly reduced after reductive leaching of BR in the presence of Fe(II). This effect was achieved due to the formation of magnetite (Fe3O4) after reductive leaching of bauxite. Magnetite is practically insoluble in H2SO4 at pH > 2. The effect of temperature (T), time (t) and liquid to solid ratio (L:S ratio) on the leaching process was revealed. The results show that under optimum conditions (pH = 2, T = 90 °C, t = 2 h, L:S ratio = 10:1), Sc extraction can reach 57%, with a simultaneous co-extraction of Fe <1.3%. At the same parameters about 10% of Fe is extracted from the raw BR. The Fe content in the residue after leaching increased from 58.3 to 66.2 wt%, corresponding to the iron concentrate. Thus, the Sc extraction from a modified BR by dilute H2SO4 creates the conditions for the complete valorization of this technogenic waste, and improved extraction selectivity.