Melilite-type Ba2MnSi2O7 was synthesized by a standard powder solid-state reaction route, and its magnetic properties were studied at low temperature. The magnetic structure was found to be C-type pointing along the c axis from neutron powder diffraction, which is different from the G-type ordering previously reported in all other 2-2-4-2 melilites with manganese as the B'-site transition metal. Ab initio (density functional theory) and magnetic dipole dipole calculations were used to understand the magnetic structure by determining the spin supersuperexchange parameters as well as the relative influence of spin orbit coupling and the magnetic dipole-dipole interactions.