The cosmic near-infrared background (NIRB) offers a powerful integral probe of radiative processes at different cosmic epochs, including the pre-reionization era during which metal-free, Population III (Pop III) stars first formed. While the radiation from metal-enriched, Population II (Pop II) stars dominates the contribution to the observed NIRB from the reionization era, Pop III stars, if formed efficiently, might leave characteristic imprints on the NIRB spectrum thanks to their strong Lyman alpha emission. Using a physically-motivated model of first star formation, we provide an updated analysis of the NIRB mean spectrum and anisotropy contributed by stellar populations at z>6. We find that in circumstances where massive Pop III stars persistently form in molecular cooling halos at a rate as high as a few times 10-3 solar masses per year, before being suppressed towards the EoR by the accumulated Lyman-Werner background, a unique spectral signature shows up redwards of 1 micron in the observed z>6 NIRB spectrum. While the detailed shape and amplitude of the spectral signature depend on various factors including the star formation histories, IMF, LyC escape fraction and so forth, the most interesting scenarios with efficient Pop III star formation are within the reach of forthcoming facilities such as the Spectro-Photometer for the History of the Universe, Epoch of Reionization and Ices Explorer (SPHEREx). As a result, new constraints on the abundance of Pop III stars during (and before) reionization will be available through precise measurements of the NIRB in the next few years.