Quantum dots consisting of an axial Zn0.97Mg0.03Te insertion inside a large-bandgap Zn0.9Mg0.1Te nanowire core are fabricated in a molecular-beam epitaxy system by employing the vapor-liquid-solid growth mechanism. In addition, this structure is coated with a thin ZnSe radial shell that forms a type-II interface with the dot semiconductor. The resulting radial electron-hole separation is evidenced by several distinct effects that occur in the presence of the ZnSe shell, including the optical emission redshift of about 250 meV, a significant decrease in emission intensity, an increase in the excitonic lifetime by one order of magnitude, and an increase in the biexciton binding energy. The type-II nanowire quantum dots where electrons and holes are radially separated constitute a promising platform for potential applications in the field of quantum information technology.