This research explores the application of germinated mung bean extract, rich in GABA (Gamma-aminobutyric acid) and polyphenols, in enhancing human health. Recognizing the instability of these bioactive compounds in environmental conditions, encapsulation emerges as a pivotal technique to broaden their applications in food and pharmaceuticals. Utilizing response surface methodology and Box–Behnken design, the freeze-drying formulation for encapsulating the aqueous extract was optimized. Second-order polynomial models were developed, exhibiting statistical adequacy in predicting key variables such as encapsulation efficiency for GABA (EE-GABA) and total polyphenol content (EE-TPC), as well as encapsulation yield for GABA (EY-GABA) and total polyphenol content (EY-TPC). The established optimal formulation was validated, resulting in predicted values for EE-GABA, EE-TPC, EY-GABA, and EY-TPC. The release kinetics of encapsulated particles were investigated, highlighting the suitability of the Korsmeyer–Peppas and Higuchi models. Assessing the stability of the encapsulated powder under varying temperatures and humidities revealed degradation rates, half-life, and activation energy, with moisture equilibrium established at 4.70%, indicative of long-term stability. In conclusion, the encapsulated germinated mung bean powder demonstrates high stability, making it a promising candidate for integration into food products and functional ingredients.