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The coupling between phonon and magnon is ubiquitous in magnetic materials and plays a crucial role in many aspects of magnetic properties, most notably in spintronics. Yet, this academically and technologically interesting problem still poses a severe challenge to a general understanding of the issue in certain materials. We report that Ni₃TeO₆ exhibits clear evidence of significant magnon-phonon coupling in both longitudinal thermal conductivity (κ_xx) and thermal Hall coefficient (κ_xy). The Debye-Callaway model, a phenomenological description for phonon heat conduction, can explain the measured magnetic field dependence of κ_xx(H) : phonon scattering from spin fluctuation in the paramagnetic phase and additional scattering due to magnon-phonon coupling in the collinear antiferromagnetic phase. We further suggest that a similar approach could be applied to understand the finite κ_xy values in Ni₃TeO₆.