Inelastic neutron scattering has been used to measure the high-energy, low-temperature magnetic excitations of the itinerant antiferromagnet FeGe₂. The spin-wave excitations follow a Heisenberg dispersion with exchange constant along the c-axis SJ_FM = 68±1 meV an order of magnitude higher than the basal-plane antiferromagnetic constant SJ_AFM = -4.4±0.6 meV. The c-axis spin waves are highly damped, even at temperatures small compared to SJ_FM. The damping is roughly quadratic in energy (as in the hydrodynamic model) up to ~250 meV, beyond which a continuum of excitations emerges.