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Previous research on the spin-phonon coupling effect mainly focuses on the renormalization of phonon frequency.Here we demonstrate that the Raman polarization selection rules of optical phonons can be greatly modified by the magnetic ordering in 2D magnet CrI₃. For monolayer samples, the dominant A_1g peak shows an abnormally high intensity in the cross-polarization channel at low temperatures, which is forbidden by the selection rule based on the lattice symmetry. For the bilayer, this peak is absent in the cross-polarization channel for the layered antiferromagnetic (AFM) state and reappears when it is tuned to the ferromagnetic (FM) state by an external magnetic field.