Adsorption of water onto metal oxide surfaces is a long-standing problem motivated by relevance to many promising technological applications. In this work, we compute the adsorption energy of water on SrTiO3 using periodic Møller-Plesset second-order perturbation theory (MP2). We compare our MP2 results to density functional and hybrid density functional theory calculations with and without the widely used D3 dispersion correction. The MP2 ground-state adsorption energy of water on SrTiO3 (001) at one monolayer coverage is 0.9 eV on the TiO2 termination in the molecular configuration and 0.6 eV in the dissociative configuration, the corresponding results on the SrO termination being 0.9 eV for both modes of adsorption. These results are reproduced well by the PBE and PBE0 exchange-correlation functionals. Correcting for dispersion effects through the D3 dispersion correction leads to significantly overestimated adsorption energies for both PBE and PBE0 with respect to MP2. The D3 correction also fails to capture the difference in electron correlation between the molecular and dissociative adsorption states, similarly to the optB86b van der Waals density functional.