Background/Objectives: Solvent-intensive methods are traditionally required to extract curcumin, a potent bioactive compound from Curcuma longa, raising environmental and safety concerns. Methods: This study introduces an efficient and scalable extraction approach using microwave–ultrasound-assisted extraction (MUAE) combined with a natural deep eutectic solvent (NADES) composed of choline chloride and lactic acid. Process parameters, including solvent water content (20–30% v/v) and solid loading (4–8% w/v), were optimized using response surface methodology (RSM) to enhance curcumin yield. Results: Under optimal conditions (20% water content and 8% solid loading), the MUAE method achieved a curcumin content of 40.72 ± 1.21 mg/g, representing a 14.36% improvement over conventional ultrasound-assisted extraction (UAE), while reducing solvent usage by 50%. The quadratic model demonstrated excellent predictive capability, with an R² value of 0.98. In addition, anti-solvent precipitation using water increased curcuminoid purity from 0.31% to 20.54%, with a recovery rate of 21.49%. Conclusions: Mechanistic analysis revealed that microwave-induced cell disruption, ultrasound cavitation, and the modulation of NADES viscosity contributed synergistically to the enhanced extraction performance. This study is the first to combine MUAE with NADES for optimized curcumin extraction, delivering both high yield and reduced solvent consumption. The proposed method offers a sustainable and industrially relevant alternative for curcumin recovery in the food, nutraceutical, and pharmaceutical sectors.