We investigate the band structure of image potential states in quasi-free-standing graphene (QFG) monolayer islands using angle-resolved two-photon-photoemission spectroscopy (AR-2PPE). Direct probing by low-energy electron diffraction (LEED) shows that QFG is formed following oxygen intercalation into the graphene-Ir(111) interface. Despite the apparent decoupling of the monolayer graphene from the Ir substrate, we find that the binding energy of the n=1 image potential state on these QFG islands increases by 0.17 eV, as compared to the original Gr/Ir(111) interface. We use calculations based on density functional theory to construct an empirical, one-dimensional potential that quantitatively reproduces the image potential state binding energy and links the changes in the interface structure to the shift in energy. Specifically, two factors, arising from the presence of intercalated oxygen adatoms, contribute comparably to this energy shift: a deeper potential well and the increase in the graphene-Ir distance associated with a wider potential well. While image potential states have not been observed previously on QFG by photoemission, our work now demonstrates that they may be strongly excited in a well-defined QFG system produced by oxygen intercalation. This opens an opportunity for studying the surface electron dynamics in QFG systems, beyond those found in typical non-intercalated graphene-on-substrate systems.