Hypervelocity stars (HVSs) discovered in the Milky Way (MW) halo are thought to be ejected from near the massive black hole (MBH) at the Galactic centre. In this paper, we investigate the spatial and velocity distributions of the HVSs which are expected to be similarly produced in the Andromeda galaxy (M31). We consider three different HVS production mechanisms: (i) the disruption of stellar binaries by the galactocentric MBH; (ii) the ejection of stars by an in-spiralling intermediate-mass black hole and (iii) the scattering of stars off a cluster of stellar-mass black holes orbiting around the MBH. While the first two mechanisms would produce large numbers of HVSs in M31, we show that the third mechanism would not be effective in M31. We numerically calculate 1.2 × 106 trajectories of HVSs from M31 within a simple model of the Local Group and hence infer the current distribution of these stars. Gravitational focusing of the HVSs by the MW and the diffuse Local Group medium leads to high densities of low-mass (≈1 M⊙) M31 HVSs near the MW. Within the virialized MW halo, we expect there to be of the order of 1000 HVSs for the first mechanism and a few hundred HVSs for the second mechanism; many of these stars should have distinctively large approach velocities (< −500 km s−1). In addition, we predict approximately five hypervelocity red giant branch (RGB) stars within the M31 halo which could be identified observationally. Future MW astrometric surveys or searches for distant giants could thus find HVSs from M31.