When CuO is cooled below its N\'eel temperature (${\mathit{T}}_{\mathit{N}2}$=213 K) the onset of long-range magnetic order effectively increases the unit-cell dimensions and additional peaks, corresponding to zone-folded phonons, appear in the Raman spectrum. The zone-folding mechanism in CuO is unusual in that one of the folded phonons hardens significantly in frequency as the sample is further cooled below ${\mathit{T}}_{\mathit{N}2}$. It is shown that this dependence on temperature is determined by the sublattice magnetization and that the unusually large shift in frequency is caused by a strong spin-phonon interaction in cupric oxide.