Cancer is a current dreadful disease and the leading cause of death. Next to cardiovascular diseases, cancer is the most severe threat to human life and health. Breast cancer is the most common invasive cancer diagnosed in women. Each year about 2.3 million women are diagnosed with breast cancer. In consideration of the severity of breast cancer, herein we designed the biocompatible nanomaterials, CNTs-HAP and GR-HAP, through grafting of hydroxyapatite (HAP) to carbon nanotubes (CNTs) and graphene (GR) nanosheets. CNTs-HAP and GR-HAP have been tested for their cytotoxicity, growth and motility inhibitory effects, and their effects on the mesenchymal markers. All these demonstrated significant dose-dependent and time-dependent in vitro cytotoxicity against SUM-159 and MCF-7 breast cancer cell lines. The cell viability assay showed that the CNTs-HAP was more effective over SUM-159 cells than MCF-7 cells. It found that the increase in the concentration of GR-HAP has inhibited the clonogenic ability of breast cancer cells. The GR-HAP exhibited a substantial inhibitory effect on the cell motility of SUM-159 cell lines. It was investigated that the expression of vimentin (mesenchymal marker) was majorly reduced in SUM-159 cells by GR-HAP.