Background: Ultrastrong magnetic fields, which can be generated transiently in relativistic heavy-ion collisions, can significantly modify the structure of finite nuclei. However, how a single-$\Lambda$ impurity embedded in a nuclear core alters the magnetic response of finite nuclei remains unclear. Purpose: To investigate the effect of a single-$\Lambda$ impurity on the magnetic response of finite nuclei, focusing on separation energies, single-particle levels, deformation, radii, and density distributions. Method: A nonrelativistic three-dimensional Skyrme-Hartree-Fock approach was employed with self-consistent coupling to an external magnetic field. The SLy4+SLL4 interaction combination was used for the main calculations, and additional SLy5+SLL4 and SLy4+LY1 results were included to assess the interaction dependence. Results: The calculations were performed for ${}_{\Lambda }^{17}O$, ${}_{\Lambda }^{29}Si$, and ${}_{\Lambda }^{41}Ca$, together with their cores, under ultrastrong magnetic fields. We analyze the effects of the Λ impurity on the core radii, deformation, single-particle spectra, and density distributions, as well as the magnetic field dependence of the Λ separation energy, root-mean-square (rms) radius, and density distribution. Under strong magnetic fields, the $\Lambda$ impurity shrinks the nucleonic density distribution, reduces the core radii, weakens the deformation response, and modifies the level-rearrangement pattern of the nuclear core. Conclusions: The single-$\Lambda$ impurity modifies the core magnetic response via the attractive $\Lambda N$ interaction and nucleonic rearrangement, while its direct magnetic coupling mainly affects the $\Lambda$ single-particle energy.