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Colloidal glasses composed of self-assembled nanoparticles can control light transport through photonic bandgaps and non-iridescent structural color, yet their phononic properties remain largely unexplored. Here, we demonstrate that colloidal glasses made of poly(methylmethacrylate) nanoparticles feature phononic bandgaps in the hypersonic (GHz) frequency range. Using momentum-resolved Brillouin light spectroscopy, the phonon dispersion relation reveals stopbands in hybrid colloidal glasses of various architectures, including gradient-ordered, gradient-mixed, binary-mixed, single-size assemblies, and bilayer structures. The observed hybridization bandgaps (HG) near 4 GHz are opened by the interactions of propagating acoustic wave packets with localized particle vibration resonances. We show that the HG bandwidth can be tuned by modifying the short-range order of the glass, while the bilayer configuration enables frequency-selective routing of acoustic waves. The results establish colloidal phononic glasses as a versatile platform for designing vibrational isolators and acoustic components of arbitrary geometry.