We investigate the electronic and magnetic properties of ͑Ga,Mn͒N nanocrystals using the density functional theory. We study both wurtzite and zinc-blende structures doped with one or two substitutional Mn impurities. For a single Mn dopant placed close to surface, the behavior of the empty Mn-induced state, hereafter referred to as "Mn hole," is different from bulk ͑Ga,Mn͒N. The energy level corresponding to this off-center Mn hole lies within the quantum-dot gap near the conduction edge. For two Mn dopants, the most stable magnetic configuration is antiferromagnetic and this result was unexpected since ͑Ga,Mn͒N bulk shows ferromagnetism in the ground state. The surprising antiferromagnetic alignment of two Mn spins is ascribed also to the holes linked to the Mn impurities that approach the surface. Unlike ͑Ga,Mn͒N bulk, these Mn holes in confined ͑Ga,Mn͒N nanostructures do not contribute to the ferromagnetic alignment of the two Mn spins.