Sharp structures in the magnetic field-dependent spin Seebeck effect (SSE) voltages of Pt/Y_{3}Fe_{5}O_{12} at low temperatures are attributed to the magnon-phonon interaction. Experimental results are well reproduced by a Boltzmann theory that includes magnetoelastic coupling. The SSE anomalies coincide with magnetic fields tuned to the threshold of magnon-polaron formation. The effect gives insight into the relative quality of the lattice and magnetization dynamics.