Terahertz scanning-probe near-field optical microscope (THz-SNOM), operating in transmission mode and relying on a flexible sapphire fiber, was developed. For this aim, a 300-μm-diameter step-index sapphire optical fiber with flat ends, high surface, and volume quality was fabricated using the edge-defined film-fed growth technique. For the lowest-order guided mode of such fiber, numerical analysis revealed small-to-moderate THz-wave propagation loss, as well as strongly subwavelength guided mode confinement in a fiber core thanks to a high refractive index of sapphire in the THz range. Experimental setup realizing the THz-SNOM principles was assembled based on thus fabricated fiber, as a probe, a backward-wave oscillator, as a continuous-wave emitter with the output wavelength of λ  =  1.2  mm, and a Golay cell, as a THz beam power detector. By combining numerical analysis and experimental study, a subwavelength resolution of our THz-SNOM setup was demonstrated. The resolution depends on orientation of the guided mode polarization toward the image plane, but always remains strongly subwavelengths and overcomes the Abbe diffraction limit. For certain orientations, it can be as low as 0.23λ. In our opinion, thanks to the subwavelength resolution, high-energy efficiency, and flexibility of design, the developed sapphire-fiber-based THz-SNOM holds strong potential in different branches of THz science and technology.