We investigate spin relaxation dynamics of interlayer excitons in a MoSe2/MoS2 heterostructure induced by the Rashba effect. In such a system, Rashba interactions arise from an out-of-plane electric field due to photogenerated interlayer excitons inducing a phonon-assisted intravalley spin relaxation. We develop a theoretical description based on a microscopic approach to quantify the magnitude of Rashba interactions and test these predictions via time-resolved Kerr rotation measurements. In agreement with the calculations, we find that the Rashba-induced intravalley spin mixing becomes the dominating spin relaxation channel above 𝑇 = 70  K. Our work identifies a previously unexplored spin-depolarization channel in heterostructures which can be used for ultrafast spin manipulation.