After Chemical Vapor Deposition (CVD), faceted structures are routinely observed on a variety of metal catalyst surfaces in the graphene-covered regions. In spite of having its bare surface flattened through high diffusivity and surface pre-melting at high temperatures, the graphene-covered copper surface still presents faceted structures. Using atomistic simulations, we show the role of graphene in the preservation of the faceted surface morphology at the graphene–copper interface, manifesting as a suppressant against surface melting and surface-specific diffusion. The results of our molecular dynamics simulations are consistent with our experimental observations and demonstrate the thermo-mechanical interfacial surface stabilization role of graphene. Our study provides an understanding applicable to most metal–graphene interfaces and is especially relevant to most metallic catalysts for graphene growth by CVD. Understanding the interaction between graphene and the catalyst surface structure is critical for producing ultra-flat and defect-free graphene.