We theoretically study the effect of the dielectric environment on the exciton ground state of CdSe and CdTe/CdSe/CdTe nanorods. We show that insulating environments enhance the exciton recombination rate and blueshift the emission peak by tens of meV. These effects are particularly pronounced for type-II nanorods. In these structures, the dielectric confinement may even modify the spatial distribution of the electron and hole charges. A critical electric field is required to separate electrons from holes, whose value increases with the insulating strength of the surroundings.