The advancing development in biomedical applications of magnetic nanoparticles leads to an increasing demand for reliable data concerning the thermophysical properties of the ferrofluids used. For applications with a relation to the flow behavior of the nanoparticle suspensions-like, e.g., magnetic drug targeting-the understanding of the basic rheological properties of the fluids under the influence of magnetic fields is of general importance. In the ongoing work presented here a magnetite-based commercial ferrofluid featuring multi-domain cores with dextran as surfactant was investigated using rotational rheometry. The analysis includes flow curve as well as yield stress measurements and reveals the magnetoviscous effect of the fluid. It has been found that significant changes of viscosity and of the overall flow behavior are induced even at low magnetic field strengths. The detected effects and therefore the changing rheological behavior of the fluid under investigation should be taken into account for further improvement of biomedical applications as well as for the synthesis of biocompatible ferrofluids.