The main aim of this study is to investigate the effect of fragmentation of electrospun carbon nanofibers (eCNFs) obtained at different temperatures, i.e., at 750 °C, 1000 °C, 1500 °C, 1750 °C and 2000 °C on the cellular response in vitro. In order to assess the influence of nanofibers on biological response, it was necessary to conduct physicochemical, microstructural and structural studies such as SEM, XPS, Raman spectroscopy, HRTEM and surface wettability of the obtained materials. During the in vitro study, all samples made contact with the human chondrocyte CHON-001 cell lines. The key study was to assess the genotoxicity of eCNFs using the comet test after 1 h or 24 h. Special attention was paid to the degree of crystallinity of the nanofibers, the dimensions of the degradation products and the presence of functional groups on their surface. A detailed analysis showed that the key determinant of the genotoxic effect is the surface chemistry. The presence of nitrogen-containing groups as a product of the decomposition of nitrile groups has an influence on the biological response, leading to mutations in the DNA. This effect was observed only for samples carbonized at lower temperatures, i.e., 750 °C and 1000 °C. These results are important with respect to selecting the temperature of thermal treatment of eCNFs dedicated for medical and environmental functions due to the minimization of the genotoxic effect of these materials.