When light either leaves or enters an optical fiber, one often needs free-space optical components to manipulate the state of polarization or the light's phase profile. It is therefore desirable to integrate such components onto a fiber end facet. In this paper, we realize, for the first time, a polarizing beam splitter fabricated directly onto the end facet of a single-mode optical fiber. The element is composed of a refractive prism, intentionally slightly displaced from the core of the fiber, and an elevated and suspended sub-wavelength diffraction grating, the lamellae of which have an aspect ratio of about 5. This integrated micro-optical component is characterized experimentally at 1550 nm wavelength. We find that the two emerging output beams exhibit a degree of polarization of 81 percent and 82 percent for Transverse Magnetic (TM) and Transverse Electric (TE) polarization, respectively.