Bauxite residue, also known as red mud (RM), from alumina production is the most promising technogenic material for the production of scandium (Sc) and other rare earth elements (REEs). Conveniently, RM is processed by using a strong acid (pH < 2.5), which lead to co-dissolution of iron and other undesirable major components. In this work, for the first time, the possibility of selective extraction of scandium from red mud by using highly diluted acid (pH > 4) in the presence of MgSO4 was shown. The effect of temperature (40–80 °C), time (0–60 min), pH (2–5), and the MgSO4 concentration (12–36 g L−1) on Sc extraction efficiency was evaluated. It was shown that Sc extraction was higher than 63% even at a pH of 4, at 80 °C, after 1 h, while more than 80% could be extracted at a pH of 2. Iron extraction reduced from 7.7 to 0.03% by increasing the pH from 2 to 4. The kinetics study using the shrinking core model (SCM) has shown that diffusion through a product layer is a rate-limiting stage of the process at high temperatures (>60 °C) and low pH (<3), whereas, at lower temperatures and higher pH values, the leaching rate is limited by diffusion through the liquid film.