A detailed analysis of the magnetic properties of a vanthoffite-type mineral Na6Mn(SO4)4 based on dc magnetization, low-temperature neutron powder diffraction, and theoretical calculations is reported. The mineral crystallizes in a monoclinic system with space group P21/c, where MnO6 octahedra are linked via SO4 tetrahedra, forming a two-dimensional (2D) sheet structure in the bc plane of the crystal. This gives rise to superexchange interaction between two Mn2+ ions mediated by two nonmagnetic bridging anions (Mn-O-O-Mn) and leads to an antiferromagnetic ordering below 3 K. The magnetic structure derived from neutron powder diffraction at 1.7 K depicts an antiferromagnetic spin arrangement in the bc plane. The magnetic properties are modeled by numerical calculations using an exact diagonalization technique, which fits the experimental results and also provides the antiferromagnetic ground state of Na6Mn(SO4)4. Both experimental and theoretical calculation reveal a quasi-2D type of magnetic interaction in this polyanionic system, where the dominant antiferromagnetic interaction exists in the plane. The determined collinear antiferromagnetic ground state is consistent with the theoretical predictions for a J1 − J2 Heisenberg triangular antiferromagnetic model.