The high loss due to the presence of strong phonon resonances makes silica fibers unfit for applications in the mid-infrared spectral range. This has led to the development of specialty optical fibers, based on novel materials and manufacturing techniques. In some cases, the characterization of these new fibers by means of standard techniques may be challenging. Fiber manufacturers would strongly benefit from a tool, which is capable of checking the geometrical and optical properties of fibers (either after fiber drawing, or even in real-time, during the drawing process). Here, we propose and demonstrate that absorption contrast X-ray computed microtomography is a non-destructive technique, capable of characterizing both geometrical and optical properties of specialty optical fibers. We experimentally verified that the tomographic intensity profile in the fiber core has the same shape as the refractive index profile, which we determined via energy-dispersed X-ray spectroscopy. We tested step- and graded-index soft glass fibers, both purchased and made in-house. Owing to the presence of high atomic number elements, which provide higher X-ray cross-section, soft glasses were more suitable than silica for their characterization via X-ray computed microtomography.