Using ab initio local spin-density-functional formalism, we study the occurrence of spin polarization in quasi-one-dimensional heterostructured C/BN nanotubes. At the zigzag boundary connecting carbon and boron nitride segments of tubes, we find atomiclike states that acquire magnetization when partly filled. Whereas individual C/BN heterojunctions can be used to spin-polarize electrons during transport, periodic arrangements of heterojunctions in doped systems can lead to the formation of a one-dimensional itinerant ferromagnetic state.