The accurate simulation of internal gravity waves (IGWs) is often hindered by spurious reflections from artificial boundaries in finite computational domains. Conventional absorbing approaches such as Rayleigh damping, characterized by adding friction terms, require thick buffer regions to suppress these reflections, increasing computational cost and reducing the usable domain. The perfectly matched layer (PML) method is an alternative damping technique based on complex coordinate stretching, commonly used to absorb outgoing waves near domain boundaries. While it performs well in wave systems where the group and phase velocities are aligned, it fails when the two velocities are in opposite directions. This situation arises for IGWs, whose distinctive dispersion relation implies that the phase and group velocities are perpendicular: the horizontal phase and group velocities are aligned, whereas their vertical components are anti-aligned. To address this issue, we develop a modified PML formulation specifically designed to handle IGWs. The method is validated using both the linear Boussinesq and anelastic equations, showing that it achieves stable, reflection‐free absorption within a narrow region and substantially reduces computational cost. This work establishes the first PML capable of absorbing IGWs and can be readily generalized to other systems where the wave phase and group velocities are in the opposite directions.