We have investigated the initial stages of growth and the electronic structure of C(60) molecules on graphene grown epitaxially on SiC(0001) at the single-molecule level using cryogenic ultrahigh vacuum scanning tunneling microscopy and spectroscopy. We observe that the first layer of C(60) molecules self-assembles into a well-ordered, close-packed arrangement on graphene upon molecular deposition at room temperature while exhibiting a subtle C(60) superlattice. We measure a highest occupied molecular orbital-lowest unoccupied molecular orbital gap of ∼3.5 eV for the C(60) molecules on graphene in submonolayer regime, indicating a significantly smaller amount of charge transfer from the graphene to C(60) and substrate-induced screening as compared to C(60) adsorbed on metallic substrates. Our results have important implications for the use of graphene for future device applications that require electronic decoupling between functional molecular adsorbates and substrates.