The epitaxial growth and preferred molecular orientation of copper phthalocyanine (CuPc) molecules on graphene has been systematically investigated and compared with growth on Si substrates, demonstrating the role of surface-mediated interactions in determining molecular orientation. X-ray scattering and diffraction, scanning tunneling microscopy, scanning electron microscopy, and first-principles theoretical calculations were used to show that the nucleation, orientation, and packing of CuPc molecules on films of graphene are fundamentally different compared to those grown on Si substrates. Interfacial dipole interactions induced by charge transfer between CuPc molecules and graphene are shown to epitaxially align the CuPc molecules in a face-on orientation in a series of ordered superstructures. At high temperatures, CuPc molecules lie flat with respect to the graphene substrate to form strip-like CuPc crystals with micrometer sizes containing monocrystalline grains. Such large epitaxial crystals may potentially enable improvement in the device performance of organic thin films, wherein charge transport, exciton diffusion, and dissociation are currently limited by grain size effects and molecular orientation.