Submarine melting has been implicated in the accelerated retreat of marine‐terminating glaciers globally. Energetic ocean flows, such as subglacial discharge plumes, are known to enhance submarine melting in their immediate vicinity. Using observations and a large eddy simulation, we demonstrate that discharge plumes emit high‐frequency internal gravity waves that propagate along glacier termini and transfer energy to distant regions of the terminus. Our analysis of wave characteristics and their correlation with subglacial discharge forcing suggest that they derive their energy from turbulent motions within the discharge plume and its surface outflow. Accounting for the near‐terminus velocities associated with these waves increases predicted melt rates by up to 70%. This may help to explain known discrepancies between observed melt rates and theoretical predictions. Because the dynamical ingredients—a buoyant plume rising through a stratified ocean—are common to many tidewater glacier systems, such internal waves are likely to be widespread.