The fundamental interactions between magnetic moments at interfaces have an important impact on the properties of layered magnetic structures. Hence, a direct probing of these interactions is highly desirable for understanding a wide range of phenomena in low-dimensional solids. Here we propose a method for probing the magnetic exchange interaction at buried interfaces using spin-polarized electrons and taking advantage of the collective nature of elementary magnetic excitations (magnons). We demonstrate that, for the case of weak coupling at the interface, the low-energy magnon mode is mainly localized at the interface. Because this mode has the longest lifetime of the modes and has a finite spectral weight across the layers on top, it can be probed by electrons. A comparison of experimental data and first-principles calculations leads to the determination of the interface exchange parameters. This method may help the development of spectroscopy of buried magnetic interfaces.