Neutron and X-ray diffraction experiments were performed on the ternary intermetallic compound YbNiSn, formerly categorized as a ferromagnetic Kondo compound. At zero field, an increase in scattering intensity was observed on top of allowed and forbidden nuclear reflections below Tc, breaking the reflection condition of the crystal symmetry Pnma. This indicates that the magnetic structure of YbNiSn is antiferromagnetic-type, rather than the previously proposed simple collinear ferromagnetic structure. Temperature dependence of the scattering intensity of the 011 reflection confirmed the magnetic ordering at 5.77(2) K. No incommensurate satellite reflection was observed at 2.5 K. By applying external magnetic field of 1 T along the a axis, the magnetic intensity at the nuclear-forbidden 001 position was suppressed, while a slight enhancement at the nuclear-allowed 002 position was observed. This suggests a spin-flip transition under the external magnetic field along the a axis in YbNiSn. The proposed magnetic structures at zero field and 1 T correspond to the magnetic space groups of Pn'm'a and Pnm'a', respectively. The piezomagnetic effect and the switch between the two magnetic space groups by the external stress, which could be detected by the anomalous Hall effect, are proposed.