We report the synthesis of single crystalline octahedron-shaped magnetite microcrystals, the preparation of magnetorheological fluids (MRFs) and their magnetorheological properties under steady-state shear conditions. The magnetite microcrystals were synthesized via the template-free hydrothermal route. MRFs with three different particle concentrations (10, 20 and 40 weight%) were prepared and were subjected to steady shear conditions at various externally applied magnetic fields of strength up to 1.2 T. The shear rates were chosen up to high enough values to observe the yield behaviour of the MRFs. The dynamic yield strengths of MRFs, estimated using the Bingham plastic model fit to the steady-state shear response curves, showed that they scale-up with the applied magnetic field strength and amount of magnetic particles in the fluid. The origin of the mechanical strength in the MRFs due to the inter-particle interaction is explained using a simple dipolar model. The observed high yield strengths of the MRFs were explained on the basis of the particle shape (octahedrons) and magnetic nature (saturation magnetization). By comparing the values of the yield strength with the on-state to off-state viscosity ratio for the MRFs (for each particle concentration), an optimum content of particles in the carrier fluid to obtain high efficiency is suggested. Because the particles are single crystalline, the off-state viscosity of the MRFs even at the highest studied (40 wt%) particle concentration was very low, which is ideal for their application as quickly responding MRFs.