Hexagonal boron nitride is an ideal dielectric to form two-dimensional heterostructures due to the fact that it can be exfoliated to be just a few atoms thick and its very low density of defects. By placing graphene nanoribbons on high quality hexagonal boron nitride it is possible to create ideal quasi-one-dimensional systems with very high mobility. The availability of high quality one-dimensional electronic systems is of great interest also given that when in proximity to a superconductor they can be effectively engineered to realize Majorana bound states. In this work we study how a boron nitride substrate affects the electronic properties of graphene nanoribbons. We consider both armchair and zigzag nanoribbons. Our results show that for some stacking configurations the boron nitride can significantly affect the electronic structure of the ribbons. In particular, for zigzag nanoribbons, due to the lock between spin and sublattice degree of freedom at the edges, the hexagonal boron nitride can induce a very strong spin splitting of the spin-polarized, edge states. We find that such spin splitting can be as high as 40 meV.