The electronic and optical properties of quasi-one-dimensional single-walled zigzag/armchair silicon-carbide nantotubes (SiC-NTs) as well as a two-dimensional SiC monolayer are investigated by ab initio methods. In order to elucidate many-electron effects on SiC nanosystems, we apply the ab initio many-body Green’s function approach to calculate the quasiparticle and optical properties of SiC nanostructures. The significant band gap correction, more than 1 eV, to the Kohn-Sham gap of density functional theory within the local density approximation of semiconducting SiC-NTs and a SiC monolayer is mainly due to the many-electron interaction effect, which is included in the GW approximation for the electron self energy. Furthermore, taking into account electron-hole interaction, the optical spectra of SiC-NTs are calculated by solving the Bethe-Salpeter equation (BSE) for the electron-hole amplitudes. Our GW+BSE calculations reveal the presence of excitons with a large binding energy as well as strong anisotropy in the optical properties in the low-dimensional SiC systems. The characteristics of the strongly bound electron-hole pairs or excitons in SiC nanostructures are also discussed in terms of the corresponding excitonic wavefunctions.