In this work we demonstrate direct van der Waals epitaxy of MoS2-graphene heterostructures on a semiconducting silicon carbide (SiC) substrate under ultra-high vacuum (UHV) conditions. Angle-resolved photoemission spectroscopy (ARPES) measurements show that the electronic structure of free-standing single-layer (SL) MoS2 is retained in these heterostructures due to the weak van der Waals interaction between adjacent materials. The MoS2 synthesis is based on a reactive physical vapor deposition (PVD) technique involving Mo evaporation and sulfurization in a H2S atmosphere on a template consisting of epitaxially grown graphene on SiC. Using scanning tunneling microscopy (STM) we study the seeding of Mo on this substrate and the evolution from nanoscale MoS2 islands to SL and bilayer (BL) MoS2 sheets during H2S exposure. Our ARPES measurements of SL and BL MoS2 on graphene reveal the coexistence of the Dirac states of graphene and the expected valence band of MoS2 with the band maximum shifted to the corner of the Brillouin zone at K in the SL limit. We confirm the 2D character of these electronic states via a lack of dispersion with photon energy. The growth of epitaxial MoS2-graphene heterostructures on SiC opens new opportunities for further in situ studies of the fundamental properties of these complex materials, as well as perspectives for implementing them in various device schemes to exploit their many promising electronic and optical properties.