Optically transparent single crystal fibers of calcium niobate (CaNb₂O₆) were investigated by polarized micro-Raman spectroscopy. The fibers were obtained by the laser heated pedestal growth technique, in the form of rods with about 0.4 mm diameter and up to 20 mm long. The crystalline axes were determined by mid-infrared reflectivity and X-ray diffraction. The fibers grew within the Pbcn columbite structure, with their longitudinal axis parallel to the crystallographic a-axis. They were free of cracks or facets, and no secondary phases were detected by the spectroscopic or structural characterizations. Polarized Raman spectra were obtained in adequate parallel and crossed configurations for the orthorhombic D_2h point group. In short, a total of 48 Raman phonon modes, which are characteristic of the CaNb₂O₆ columbite crystal, were discerned, in good agreement with group theoretical predictions. The selection rules for the columbite group were generally well obeyed, confirming the high purity, ordering, and quality of the material. The knowledge of the optical phonon characteristics of the CaNb₂O₆ single crystals presented here is important to design compact optical devices, such as solid-state lasers operating in the near-infrared region.