Edge states in narrow quasi-two-dimensional nanostructures determine, to a large extent, their electric, thermoelectric, and magnetic properties. Nonmagnetic edge states may quite often lead to topological-insulator-type behavior. However, another scenario develops when the zigzag edges are magnetic and the time reversal symmetry is broken. In this work we report on the electronic band structure modifications, electrical conductance, and thermoelectric properties of narrow zigzag nanoribbons with spontaneously magnetized edges. Theoretical studies based on the Kane-Mele-Hubbard tight-binding model show that for silicene, germanene, and stanene both the Seebeck coefficient and the thermoelectric power factor are strongly enhanced for energies close to the charge neutrality point. A perpendicular gate voltage lifts the spin degeneracy of energy bands in the ground state with antiparallel magnetized zigzag edges and makes the electrical conductance significantly spin polarized. Simultaneously the gate voltage worsens the thermoelectric performance. Estimated room-temperature figures of merit for the aforementioned nanoribbons can exceed a value of 3 if phonon thermal conductances are adequately reduced.