We have investigated nanocrystals of Fe(IO3)3 by polarization-sensitive second harmonic generation (SHG) microscopy. As the nonlinear optical properties of this material were only poorly characterized, we have first determined the relative values of the elements of its second-order susceptibility tensor, by the global fitting of the polarization-resolved SHG response of an ensemble of nanocrystals. This information allows one to optically retrieve the orientation of individual particles in the sample. The high SHG efficiency measured for nanocrystals of Fe(IO3)3 and their polar nature could make them very attractive for nonlinear microscopy of biological samples.