Significant changes in the Raman spectrum of single-layer graphene grown on a copper film were observed after the spontaneous oxidation of the underlying substrate that occurred under ambient conditions. The frequencies of the graphene G and 2D Raman modes were found to undergo red shifts, while the intensities of the two bands change by more than an order of magnitude. To understand the origin of these effects, we further characterized the samples by scanning tunneling microscopy (STM), scanning tunneling spectroscopy (STS), and atomic force microscopy (AFM). The oxidation of the substrate produced an appreciable corrugation in the substrate without disrupting the crystalline order of the graphene overlayer and/or changing the carrier doping level. We explain the red shifts of the Raman frequencies in terms of tensile strain induced by corrugation of the graphene layer. The changes in Raman intensity with oxidation arise from the influence of the thin cuprous oxide film on the efficiency of light coupling with the graphene layer in the Raman scattering process.