Hard-magnetic plate-like nanoparticles of SrFe12O19 were synthesised hydrothermally. The particles, fixed in a polymer, exhibited a coercivity in the range 0.9–1.8 kOe, and the saturation magnetization values reached 64 emu g−1. Electrostatically stabilized aqueous colloidal solutions of the plate-like particles with average thickness of 5–8 nm and average diameter of 30–80 nm were prepared. The nanoparticles readily oriented when applying a weak magnetic field as low as a few Oe, and due to the linear dichroism phenomena a strong change in the optical transmittance of the solution took place. The extinction coefficient ratio for the perpendicular and the parallel light's electric field vector relative to the magnetic field direction was found to be up to 4.5. The experimental results were compared with a theoretical model, in which the optical absorption of the nanoparticles was calculated from the polarizability of oblate ellipsoids.