Resonant plasmonic excitations in micro-scale structures at terahertz (THz) frequencies can make a large impact development of THz devises. A number of material systems have been proposed and demonstrated for THz plasmonic resonators, including doped semiconductors, materials with metallic behavior, such as graphene, graphite, and carbon nano-tubes, superconductors and topological insulators. However, experimental investigations of THz plasmonic resonators, which are typically a fraction of the free space wavelength in size, remain challenging. We demonstrate that THz near-field spectroscopy and imaging technique based on a subwavelength aperture probe can be employed to detect excitation of THz plasmons in carbon micro-fibers. Upon excitation of a single carbon fiber by a THz pulse, we observe a standing wave formed along the fiber length. The resonant frequency is consistent with the fundamental dipole mode, both in its value and in its dependence on the fiber length. The field of the standing wave is localized and it indicates the plasmonic nature of the excitation. The fact that the resonance frequency also depends on the material conductivity allows us to employ the THz near-field spectroscopy method to evaluate the material conductivity non-invasively. Furthermore we propose an alternative method for non-contact conductivity probing. It utilizes the relative amplitude of the surface plasmon field that can be measured by the near-field probe. The amplitude increases with the fiber conductivity and therefore it can be used for conductivity estimation.