Abstract The existence of mutually correlated thin and rotating planes of satellite galaxies around both the Milky Way (MW) and Andromeda (M31) calls for an explanation. Previous work in Milgromian dynamics (MOND) indicated that a past MW-M31 encounter might have led to the formation of these satellite planes. We perform the first-ever hydrodynamical MOND simulation of the Local Group using phantom of ramses. We show that an MW-M31 encounter at z ≈ 1, with a perigalactic distance of about 80 kpc, can yield two disc galaxies at z = 0 oriented similarly to the observed galactic discs and separated similarly to the observed M31 distance. Importantly, the tidal debris are distributed in phase space similarly to the observed MW and M31 satellite planes, with the correct preferred orbital pole for both. The MW-M31 orbital geometry is consistent with the presently observed M31 proper motion despite this not being considered as a constraint when exploring the parameter space. The mass of the tidal debris around the MW and M31 at z = 0 compare well with the mass observed in their satellite systems. The remnant discs of the two galaxies have realistic radial scale lengths and velocity dispersions, and the simulation naturally produces a much hotter stellar disc in M31 than in the MW. However, reconciling this scenario with the ages of stellar populations in satellite galaxies would require that a higher fraction of stars previously formed in the outskirts of the progenitors ended up within the tidal debris, or that the MW-M31 interaction occurred at z > 1.