We show that a spontaneous magnetic moment may appear at the edge of a spin-triplet superconductor if the system allows for pairing in a subdominant channel. To unveil the microscopic mechanism behind such an effect, we combine numerical solution of the Bogoliubov-de Gennes equations for a tight-binding model with nearest-neighbor attraction, and the symmetry based Ginzburg-Landau approach. We find that a potential barrier modulating the electronic density near the edge of the system leads to a nonunitary superconducting state close to the boundary where spin-singlet pairing coexists with the dominant triplet superconducting order. We demonstrate that the spin polarization at the edge appears due to the inhomogeneity of the nonunitary state and originates in the lifting of the spin degeneracy of the Andreev bound states.