The recently discovered metal-malonate compounds of formulae Na2M(H2C3O4)2·2H2O with M = Mn, Fe, Co, Ni are investigated for their magnetic properties. While the Cu-based material is a weak ferromagnet, all other members present antiferromagnetic interactions. Neutron powder diffraction experiments reveal the establishment of a long range magnetic order at low temperature in the Pbca Shubnikov magnetic group. The magnetic structures are characterized by antiferromagnetic layers perpendicular to [001]. These layers are stacked antiparallel (M = Fe) or parallel (M = Mn, Ni) in the (a, c) plane. Magnetic moments are collinear to b for the former and to c for the latter. The M = Co malonate exhibits a non-collinear magnetic structure intermediate between the two latter, with components along b and c. Density functional theory calculations indicate that the dominant magnetic interaction, J1, occurs along a malonate group via a carboxylate and links two transition metals within the same layer, while other interactions (inter- or intra-layer) are much weaker, so that these compounds present the dominant characteristics of 2D-antiferromagnets.