Heterostructures, composed of semiconducting transition-metal dichalcogenides (TMDC) and magnetic van-der-Waals materials, offer exciting prospects for the manipulation of the TMDC valley properties via proximity interaction with the magnetic material. We show that the atomic proximity of monolayer MoSe2 and the antiferromagnetic van-der-Waals crystal CrSBr leads to an unexpected breaking of time-reversal symmetry, with originally perpendicular spin directions in both materials. The observed effect can be traced back to a proximity-induced exchange interaction via first-principles calculations. The resulting spin splitting in MoSe2 is determined experimentally and theoretically to be on the order of a few meV. Moreover, we find a more than 2 orders of magnitude longer valley lifetime of spin-polarized charge carriers in the heterostructure, as compared to monolayer MoSe2/SiO2, driven by a Mott transition in the type-III band-aligned heterostructure.