The design of single-molecule photoswitchable emitters was the first milestone toward the advent of single-molecule localization microscopy that sets a new paradigm in the field of optical imaging. Several photoswitchable emitters have been developed but they all fluoresce in the visible or far-red ranges, missing the desirable near-infrared window where biological tissues are most transparent. Moreover, photocontrol of individual emitters in the near-infrared would be highly desirable for elementary optical molecular switches or information storage elements since most communication data transfer protocols are established in this spectral range. Here we introduce a novel type of hybrid nanomaterials consisting of single-wall carbon nanotubes covalently functionalized with photo-switching molecules that are used to control the intrinsic luminescence of the single nanotubes in the near-infrared (beyond 1 $\mu$m). We provide proof-of-concept of localization microscopy based on these bright photoswitchable near-infrared emitters.