The aim of this work has been the investigation of the anisotropy of the viscosity of a ferrofluid with magnetically interacting particles which are able to form structures in an applied magnetic field. The results of the experiments show a significant deviation from the case of a fluid without strong dipolar interactions. Furthermore, we have determined the dependence of the ratio of the viscosity coefficients on shear rate providing an insight into the microstructural reasons for the observed effects.