Using first-principles calculations, the effect of magnetic point defects (vacancy and adatom) is investigated in zigzag graphene nanoribbons. The structural, electronic, and spin-transport properties are studied. While pristine ribbons display anti-parallel spin states at their edges, the defects are found to perturb this coupling. The introduction of a vacancy drastically reduces the energy difference between parallel and anti-parallel spin orientations, though the latter is still favored. Moreover, the local magnetic moment of the defect is screened by the edges so that the total magnetic moment is quite small. In contrast, when an adatom is introduced, the parallel spin orientation is preferred and the local magnetic moment of the defect adds up to the contributions of the edges. Furthermore, a spin-polarized transmission is observed at the Fermi energy, suggesting the use of such a defective graphene nanoribbon as spin-valve device.