This study aimed to use eggplant peels as a potential source of anthocyanins with biological activities. Two different extraction methods were tested in order to obtain extracts with a high anthocyanin content. The selected methods were the solid–liquid extraction (SLE) and ultrasound-assisted extraction (UAE) methods. For each method, two concentrations of ethanol (EtOH) were used, while varying the extraction time and temperature. Based on the results, the extracts obtained by SLE using EtOH 96% after 30 min of extraction at 50 °C showed the highest anthocyanin concentration. The UAE allowed the best results with EtOH 96% after 30 min at 25 °C. Both selected extracts showed similar chromatographic profiles, with delphinidin 3-O-rutinoside as the major anthocyanin, but in a higher concentration in UAE. The extracts also presented inhibitory activity against lipoxygenase (LOX), lipase, and α-amylase, thus suggesting a possible involvement in reducing the risk of various disorders. The first order kinetic model was used to predict the changes that can occur in the anthocyanin content and antioxidant activity from the eggplant peel extract. The calculated kinetic and thermodynamic parameters confirm the irreversible degradation of phytochemicals.