The annihilation of dark matter (DM) particles in the Milky Way can contribute to the diffuse gamma-ray background (DGRB). Due to the presence of substructures, this emission will appear anisotropic in a predictable way. We generate full-sky maps of the gamma-ray emission in galactic substructures from results of the high-resolution Via Lactea II N-body simulation of the Milky Way DM halo. We calculate the anisotropy pattern, taking into account different radial profiles of the DM distribution in substructures, cosmic variance, and the detection threshold, and compare it to the anisotropy in the DGRB observed by the Fermi Large Area Telescope (LAT). By comparing the upper limits on the DM self-annihilation cross-section, <$\sigma v$>, implied by the anisotropy to the intensity of the DGRB and detected sources in the LAT 2-yr Point Source Catalog, we find that galactic substructure cannot contribute to the anisotropies in the DGRB without strongly violating these observations. Our results challenge the perception that small-scale anisotropies in the DGRB can be used as a probe of DM annihilation in galactic subhaloes.