In this study, a surface acoustic wave (SAW) resonator coated with graphene/polypyrrole hybrid nanocomposite films decorated with silver nanoparticles (AgNPs-G/PPy) is proposed for detecting ammonia (NH3) in parts-per-billion concentrations. The AgNPs-G/PPy hybrid nanocomposite film was synthesized via in situ chemical oxidative polymerization. Scanning electron microscopy, energy-dispersive X-ray spectroscopy, and X-ray diffraction were used to characterize the AgNPs-G/PPy hybrid nanocomposite film, confirming its successful synthesis and identifying a wrinkled multilayered structure. The AgNPs-G/PPy hybrid nanocomposite film was spin-coated onto the surface of a stress-compensated temperature-cut quartz SAW resonator having an operating frequency of 98.5 MHz to create an NH3 gas sensor. NH3 adsorption by the AgNPs-G/PPy hybrid nanocomposite film modulated the acoustic wave velocity, and the corresponding frequency shift served as a sensing signal. The synergistic interaction between the three constituent materials (AgNPs, graphene, and polypyrrole) enhanced the sensitivity, selectivity, and response speed of the sensor for NH3 detection. At room temperature, the proposed sensor exhibited a positive frequency shift of 568 Hz when exposed to 50 ppb of NH3 gas and a rapid response time of less than 60 s. In addition, the SAW sensor exhibited excellent selectivity.