We demonstrate that thousands of periodic nano-craters are fabricated on a subwavelength-diameter tapered optical fiber, an optical nanofiber, by irradiating with just a single femtosecond laser pulse. A key aspect of the fabrication is that the nanofiber itself acts as a cylindrical lens and focuses the femtosecond laser beam on its shadow surface. We also demonstrate that the periodic nano-crater array on the nanofiber shows polarization dependent fiber Bragg grating (FBG) characteristics. Such FBG structures on the nanofiber may act as a 1-D photonic crystal due to the strong transverse and longitudinal confinement of the field.