Proximity effects induced in the two-dimensional Dirac material graphene potentially open access to novel and intriguing physical phenomena. Thus far, the coupling between graphene and ferromagnetic insulators has been experimentally established. However, only very little is known about graphene's interaction with antiferromagnetic insulators. Here, we report a low-temperature study of the electronic properties of high quality van der Waals heterostructures composed of a single graphene layer proximitized with alpha-RuCl3. The latter is known to become antiferromagnetically ordered below 10 K. Shubnikov-de Haas oscillations in the longitudinal resistance together with Hall resistance measurements provide clear evidence for a band realignment that is accompanied by a transfer of electrons originally occupying the graphene's spin degenerate Dirac cones into alpha-RuCl3 band states with in-plane spin polarization. Left behind are holes in two separate Fermi pockets, only the dispersion of one of which is distorted near the Fermi energy due to spin selective hybridization with these spin polarized alpha-RuCl3 band states. This interpretation is supported by our density functional theory calculations. An unexpected damping of the quantum oscillations as well as a zero-field resistance upturn close to the Neel temperature of alpha-RuCl3 suggest the onset of additional spin scattering due to spin fluctuations in the alpha-RuCl3.