We studied the local optical response of semiconducting single-walled carbon nanotubes to wrapping by DNA segments using high resolution tip-enhanced near-field microscopy. Photoluminescence (PL) near-field images of single nanotubes reveal large DNA-wrapping-induced red shifts of the exciton energy that are two times higher than indicated by spatially averaging confocal microscopy. Near-field PL spectra taken along nanotubes feature two distinct PL bands resulting from DNA-wrapped and unwrapped nanotube segments. The transition between the two energy levels occurs on a length scale smaller than our spatial resolution of about 15 nm