The development of functional fermented beverages enriched with γ-aminobutyric acid (GABA) has been pursued because of the health benefits of GABA; however, few studies have described GABA production by yeast. Therefore, this study aimed to produce fermented apple beverages enriched with GABA produced by Saccharomyces cerevisiae SC125. Golden Delicious apples were fermented by S. cerevisiae SC125 to produce a novel functional beverage; commercial yeast was used as the control. The GABA, organic acid, and volatile compound content during the fermentation process was investigated by high-performance liquid chromatography and headspace solid-phase microextraction/gas chromatography-mass spectrometry. A yield of 898.35 ± 10.10 mg/L GABA was achieved by the efficient bioconversion of L-monosodium glutamate. Notably, the S. cerevisiae SC125-fermented beverage produced several unique volatile compounds, such as esters, alcohols, 6-decenoic acid, and 3-hydroxy−2-butanone, and showed significantly enhanced contents of organic acids, including malic acids, citric acid, and quinic acid. Sensory analysis demonstrated that the S. cerevisiae SC125-fermented apple beverage had improved aroma, flavor, and overall acceptability. In conclusion, a fermented functional apple beverage containing GABA was efficiently produced using S. cerevisiae SC125.