The structural stability, together with the electronic and magnetic properties of zigzag boron nitride nanoribbons (ZBNNRs) with single vacancy defects and doped with ten 3d transition metal (TM) species was investigated using spin-polarized density functional theory (DFT). The results on the formation energy show that the structural stability of the ZBNNRs with single vacancy defects decreases significantly when compared to pristine nanoribbons. Moreover, the ZBNNRs with the N-site vacancy defects are generally more stable than those with the B-site ones. By conducting the ab initio molecular dynamic simulations, the ZBNNRs with the 4B-site or 4N-site vacancy defects are both shown to be stable at room temperature. Among the BN nanoribbons doped with ten different TM ions, the structural stability of the Sc-, Ti-, and V-doped systems appears to be improved, whereas the Cr-, Mn-, Fe-, Co-, Ni-, Cu-, and Zn-doped ZBNNRs are unstable when compared to the pristine ZBNNRs. The vacancy defects and the substitutional doping via 3d TM atoms, excluding the scandium atom, exhibit a magnetic effect in non-magnetic ZBNNRs. The difference charge density diagrams indicate that during the doping process, the electrons mainly transfer from the transition metal ions to their three adjacent N atoms.