We report structural studies on the epitaxial growth of GaAs/GaNAs core-shell nanowires (NWs) on patterned Si (111) substrates by self-catalyzed selective area growth using Gas-Source Molecular Beam Epitaxy. Epitaxial growth conditions were obtained using a combination of dry and time-sensitive wet etching of the SiO2 growth mask and native SiO2 layer, respectively. We found that higher growth temperatures resulted in a higher yield for the epitaxial growth of patterned self-catalyzed GaAs NWs on Si with an optimal temperature of 690 °C. The GaNAs shell growth at 500 °C was found to be conformal and maintained an epitaxial and dislocation-free interface with both the Si substrate and the GaAs nanowire. The micro-photoluminescence (μ-PL) measurement at 6 K revealed two bands peaking at 1.45 and 1.17 eV, which could be emission from the GaAs core and GaNAs shell. Transmission electron microscopy showed the zincblende crystal structure of GaAs and GaAs/GaNAs core-shell NWs with minimal twinning near the base of the GaAs nanowires and at the tips of the GaAs/GaNAs core/shell nanowires. This study illustrates the feasibility of the epitaxial growth of patterned GaAs with dilute nitride shells on Si substrates, which would have potential for Si-friendly intermediate band solar cells and telecom emitters.