This paper presents the results of an experimental study of the influence of an external magnetic field on the shear flow behaviour of a magnetic fluid based on barium hexaferrite nanoplates. With the use of rheometry, the magnetoviscosity and field-dependent yield-stress in the fluid are evaluated. The observed fluid behaviour is compared to that of ferrofluids with magnetic nanoparticles having high dipole interaction. The results obtained supplement the so-far poorly studied topic of the influence of magnetic nanoparticles’ shape on magnetoviscous effects. It is concluded that the parameter determining the observed magnetoviscous effects in the fluid under study is the ratio V²/l³, where V is the volume of the nanoparticle and l is the size of the nanoparticle in the direction corresponding to its orientation in the externally applied magnetic field.