Pectin was extracted from apple (Malus domestica ‘Fălticeni’) pomace with Celluclast 1.5L, at doses of 20, 40, and 60 µL/g of material. The temperature and time of extraction were varied on three levels—temperature—40, 50, and 60 °C; time—12, 18, and 24 h. For each experiment, the extraction yield (R2 = 0.8905), the galacturonic acid content (R2 = 0.9866), and the degree of esterification (R2 = 0.9520) of pectin was determined. Response surface methodology (RSM) was implemented via a Box–Behnken design, to optimize pectin extraction. In the optimum extraction conditions (temperature of 48.3 °C, extraction time of 18 h 14 min, and enzyme dose of 42.5 µL/g of pomace), the design predicted a 6.76% yield with a galacturonic acid content of 97.46 g/100 g of pectin and a degree of esterification of 96.02%. FT-IR analysis of the pectin sample obtained in these conditions showed a chemical structure similar to that of commercial apple and citrus pectin.