In this work, the solid–liquid extraction of bioactive molecules from grape skin was performed using water as the extraction solvent. The effects of extraction time (t = 60, 75, and 90 min), extraction temperature (T = 40, 60, and 80 °C), solid–liquid phase ratio (S/L = 10, 20, and 30 g/L), and mixing speed (rpm = 250, 500, and 750 1/min) on the total dissolved solids, extraction yield, concentration of total polyphenols, and antioxidant activity were determined using the 1,1-diphenyl-2-picrylhydrazyl (DPPH) and ferric reducing antioxidant power (FRAP) methods. According to response surface modeling, the optimal extraction conditions were t = 75 min, T = 80 °C, S/L = 30 g/L, and rpm = 750 1/min, and under optimal process conditions, 8.38 mgGAE/gd.m. was obtained. Furthermore, the potential of near-infrared (NIR) spectroscopy coupled with artificial neural network (ANN) modeling for prediction of the physical and chemical properties of prepared extracts was also analyzed. The use of ANN modeling demonstrated highly favorable correlations between the NIR spectra and all the variables tested, particularly the total dissolved solids (TDS) and antioxidant activity measured using the FRAP method. As a result, ANN modeling proved to be a valuable tool for predicting the concentration of total polyphenols, the antioxidant activity, and the extraction yield of a plant extract based on its NIR spectra.