We set new limits on the global shape of the dark halo in the Andromeda galaxy based on axisymmetric mass models constructed by Hayashi & Chiba (2012). This is motivated by the fact that CDM models predict non-spherical virialized dark halos, which reflect the process of mass assembly in the galactic scale. Based on the application of our models to latest kinematical data of globular clusters and dwarf spheroidal galaxies in the Andromeda halo, we find that the most plausible cases for Andromeda yield not a spherical but a prolate shape for its dark halo. We also find that the prolate dark halo is consistent with theoretical predictions in which the satellites are distributed anisotropically and preferentially located along major axes of their galactic host halos. It is a reflection of the intimate connection between galactic dark matter halos and the cosmic web.