The factors affecting the efficiency of micelle-mediated extraction of phenolic compounds from apple pomace was investigated. Higher extraction efficiency by using as a solvent an aqueous solution of Tween 80 in comparison to Triton X-100, Span 20, Tween 20, 70% ethanol, and water was shown. Four independent variables (Tween 80 concentration, time, solvent-to material ratio, and pH) to enhance the recovery of polyphenols from apple pomace was investigated. Applying response surface methodology, the second order polynomial regression equation showing dependence of the yield of polyphenols on the extraction parameters was derived. The adjusted regression coefficient (R2 = 98.73%) and the lack-of-fit test (p > 0.05) showed a good accuracy of the developed model. The difference between observed and predicted values was no more than 3%. The optimal extraction conditions were found to be Tween 80 concentration of 1.14%, time of 65 min, solvent-to-material ratio of 104 mL g−1, pH of 3.8. Under optimal conditions the predicted total phenolic compounds content was 7.75 mg g−1. The obtained apple pomace extracts were characterized in terms of their antioxidant activity. The proposed extraction technology by using Tween 80 aqueous solution as a solvent allows obtaining the extracts with high content of polyphenols which are suitable for the applications in food, cosmetic, and pharmaceutical products requiring a surfactant to stabilize them.