A phonoriton is an elementary excitation that is predicted to emerge from hybridization between exciton, phonon, and photon. Besides the intriguing many-particle structure, phonoritons are of interest as they could serve as functional nodes in devices that utilize electronic, phononic, and photonic elements for energy conversion and thermal transport applications. Although phonoritons are predicted to emerge in an excitonic medium under intense electromagnetic wave irradiation, the stringent condition for their existence has eluded direct observation in solids. In particular, on-resonance, intense pumping schemes have been proposed, but excessive photoexcitation of carriers prevents optical detection. Here, we theoretically predict the appearance of phonoritonic features in monolayer hexagonal boron nitride (h-BN) embedded in an optical cavity. The coherent superposition nature of phonoriton states is evidenced by the hybridization of exciton-polariton branches with phonon replicas that is tunable by the cavity-matter coupling strength. This finding simultaneously provides an experimental pathway for observing the predicted phonoritons and opens a new avenue for tuning materials properties.