The electronic properties of graphene on top of ferroelectric HfO2 substrates in an orthorhombic phase with space group Pca21 are investigated using density functional theory calculations. The space group Pca21 was recently identified as one of the two potential candidates for ferroelectricity in hafnia, with the polarization direction oriented along the [001] direction. Our results indicate the appearance of sizable energy gaps in graphene induced by the HfO2 substrate, as a consequence of orbital hybridization and the locally deformed graphene structure. The gap sizes depend on the type of HfO2 termination interacting with graphene, showing larger gaps for oxygen terminated slabs compared to hafnium terminated ones. These observations may prove to be highly significant for the development of graphene based field effect transistors using high-k dielectrics.