The main objective of this work was to extract antioxidant compounds from by-products from the mango processing industry by means of microwave-assisted extraction (MAE). For this, two steps were proposed, first, a kinetics modeling, and then a Box–Behnken design to study the effect of the variables time, power and ethanol concentration on the responses: total extraction yield (TEY), total phenolic content (TPC), total flavonoids content (TFC), and total carotenoids content (TCC). In the kinetics study, all models described a high correlation with the experimental data from bioactive compounds extraction from mango peel. Among these, the two-site mathematical model better described the experimental data (R2 > 95%). Optimization results using response surface methodology have shown great adjustments to the quadratic models for TPC, TFC, and TCC; showing that the Box–Behnken design for this subject of research can be of great use when it does not comply with the technical conditions to realize a central design. Practical Applications: The present study focused on the mathematical modeling of microwave-assisted extraction of bio-compounds from industrial mango peel by-products. Modeling tools such as kinetics studies or response surface methodologies allow the optimization of extraction and process cost reduction. Extracts were obtained at high yield regarding phenolics, flavonoids, and carotenoids content, with high antioxidant activity. These results show that extracts with high antioxidant properties may be applicable in a wide range of foods.