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It may be possible that the optical phonon of the 5d pyrochlore iridates can be renormalized due to the Dzyloshinskii-Moriya (DM) Hamiltonian. In this study, the evidence for unconventional spin-phonon interaction in Y₂Ir₂O₇ was identified by infrared spectroscopy and first-principles calculations. The measured infrared phonon frequencies were suddenly shifted near the Néel temperature of the exotic all-in-all-out magnetism indicating the presence of spin-phonon interaction. From calculations, this phonon renormalization was well-described as a modulation of the basis Ir-O-Ir bond angle. It was also found that the DM interaction was strongly modulated by the basis Ir-O-Ir bond angle. This indicates that DM interaction is the major origin of phonon renormalization. This spin-phonon interaction in Y₂Ir₂O₇ is possible due to the inherently strong SOI and consequently can be realized in pyrochlore structures. This spin-phonon coupling via DM interaction is distinguished from the conventional picture of the spin-phonon coupling mechanism via super-exchange interaction.