Atom-like defects in two-dimensional (2D) hexagonal boron nitride (hBN) have recently emerged as a promising platform for quantum information science. Here, we investigate single-photon emissions from atomic defects in boron nitride nanotubes (BNNTs). We demonstrate the first, to the best of our knowledge, optical modulation of the quantum emission from BNNTs with a near-infrared laser. This one-dimensional system displays a bright single-photon emission, as well as high stability at room temperature, and is an excellent candidate for optomechanics. The fast optical modulation of a single-photon emission shows multiple electronic levels of the system and has potential applications in optical signal processing.