Increasing requirements for environmental protection have led to the need for the development of control systems for exhaust gases monitored directly at high temperatures in the range of 300–800 °C. The development of high-temperature gas sensors requires the creation of new materials that are stable under these conditions. The stability of nanostructured semiconductor oxides at high temperature can be enhanced by creating composites with highly dispersed silicon carbide (SiC). In this work, ZnO and SiC nanofibers were synthesized by electrospinning of polymer solutions followed by heat treatment, which is necessary for polymer removal and crystallization of semiconductor materials. ZnO/SiC nanocomposites (15–45 mol % SiC) were obtained by mixing the components in a single homogeneous paste with subsequent thermal annealing. The composition and microstructure of the materials were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), Fourier-transform infrared spectroscopy (FTIR) and X-ray photoelectron spectroscopy (XPS). The electrophysical and gas sensing properties of the materials were investigated by in situ conductivity measurements in the presence of the reducing gases CO and NH3 (20 ppm), in dry conditions (relative humidity at 25 °C RH25 = 0) and in humid air (RH25 = 30%) in the temperature range 400–550 °C. The ZnO/SiC nanocomposites were characterized by a higher concentration of chemisorbed oxygen, higher activation energy of conductivity, and higher sensor response towards CO and NH3 as compared with ZnO nanofibers. The obtained experimental results were interpreted in terms of the formation of an n–n heterojunction at the ZnO/SiC interface.