Altermagnets' (AMs) non-relativistic spin splitting enables novel states, spintronic and magneto-optical devices, though their optical signatures remain elusive. Here, we report exciton-magnon emission and absorption: optical sidebands from a spin-forbidden dark exciton, a direct consequence of altermagnetic symmetry. Combined optical spectroscopy and first-principles calculations reveal that La₂O₃Mn₂Se₂ is an altermagnetic insulator, hosting a strongly bound, spin-forbidden dark exciton and a higher-energy bright exciton. Photoluminescence (PL) and absorption reveal mirror-image sidebands, Stokes-shifted in emission and anti-Stokes-shifted in absorption, symmetric about the dark exciton, whose energy shifts and spectral shapes match the magnon energy scale and density of states measured independently by inelastic neutron scattering. The PL intensity tracks the full equal-time spin-spin correlator, combining static and dynamical contributions, and rules out alternative processes. This directly couples PL to magnetism, with potential for magneto-optical devices. These results establish exciton-magnon spectroscopy as a new route for optically identifying and exploiting AMs.