The study conducts an experimental analysis of the response of diluted magnetic suspensions with nano- and micro-sized particles structured in an external magnetic field to a quasi-static shear strain applied perpendicular to the direction of the external magnetic field. Magnetic rheometry is used as the research method. For microparticle-based composites, X-ray computed microtomography is used to evaluate qualitatively the morphology of particle aggregates induced in the suspension. It is found that a structured magnetic suspension based on nanoparticles with a volume concentration of around 1–2% demonstrates a non-monotonic response with an overshoot. Conversely, more concentrated suspensions with nanoparticles as well as suspensions of microparticles with a similar particle volume fractions exhibit monotonic dependencies of shear stress on quasi-static shear strain. A non-monotonic stress–strain relationship was also observed for highly diluted suspensions of magnetic microparticles (∼ 0.1%) under certain experimental conditions. The results obtained form the basis for refining, further developing, and testing the corresponding theoretical concepts.