The Ge core-level shift across the Ge/GeO2 interface is determined within semilocal and hybrid density functional schemes. We first assess the accuracy achieved within these theoretical frameworks by comparing calculated and measured core-level shifts for a set of Ge-based molecules. The comparison with experimental data results in rms deviations of 0.19 and 0.09 eV for core-level shifts calculated with semilocal and hybrid density functionals, respectively. We also compare calculated core-level shifts at the Ge(001)-c(4 x 2) surface with high-resolution x-ray photoemission spectra finding similar agreement. We then turn to the Ge/GeO2 interface, which we describe with atomistic superlattice models showing alternating layers of Ge and GeO2. The adopted models include a substoichiometric transition region in which all Ge atoms are fourfold coordinated and all O atoms are twofold coordinated, as inferred for Si/SiO2 interfaces. Since the calculation of core-level shifts involves charged systems subject to finite-size effects, we use two different methods to ascertain the core-level shift Delta E-XPS between the oxidation state Ge-0 and Ge+4 across the interface. In the first method, core-hole relaxations are first evaluated in bulk models of the interface components and then complemented by the initial-state shift calculated across the interface, while the second method consists of direct interface calculations corrected through classical electrostatics. Using the more accurate hybrid functional scheme, we obtain a shift Delta E-XPS of 2.7 +/- 0.1 eV. This value is significantly lower than experimental data, which typically fall around 3.3 eV or higher, but the underestimation is consistent with that found for the valence band offset of the same model. This leads to the conclusion that the adopted model structures yield an incorrect description of the interface dipole and emphasizes that Ge/GeO2 interfaces possess different structural properties than their silicon counterparts.