Antiferromagnetic ordering and structural phase transition have been investigated via comprehensive neutron and x-ray diffraction on Sn-flux-grown BaFe₂As₂ single crystals, the A-122 family of FeAs-based high-TC superconductor compounds. The incorporation of Sn in the lattice resulted to an average composition of Ba_0.95Sn_0.05Fe₂As₂. A tetragonal-to-orthorhombic structural phase transition and a three-dimensional longrange antiferromagnetic ordering of the iron magnetic moment, with a unique magnetic propagation wave vector k=(1,0,1) have been found to take place at ~90 K. The magnetic moments of iron are aligned along the longer a axis in the low-temperature orthorhombic phase (Fmmm with b<a<c<. Our results thus demon strate that the magnetic structure of the Sn-flux-grown BaFe₂As₂ single crystal is the same as those in the polycrystalline samples and in other A-122 iron pnictides compounds.We argue that the Sn incorporation in the lattice is responsible for a smaller orthorhombic splitting and lower Néel temperature TN observed in the experiments.