The structural and magnetic properties of BaMn2Si2O7 have been investigated. The magnetic susceptibility and specific heat, measured using single crystals, suggest that the quasi-one-dimensional magnetism originating from the loosely coupled Mn2+ chain carrying S=5/2 is present at high temperatures, which is similar to the other quasi-one-dimensional barium silicates, BaM2Si2O7 (M: Cu and Co). The Neel temperature (TN=26 K) is high compared to the magnetic interaction along the chain (J = -6 K). The neutron powder diffraction study has revealed that the magnetic structure is long-ranged with antiferromagnetic arrangement along the chain (c) direction and ferromagnetic arrangement along the a and b axes. The detailed structural analysis suggests that the interchain interaction via Mn-O-Mn bond along the a axis is relatively large, which makes the system behave more two-dimensionally in the ac plane and enhances TN.