Melittin, as an agent to lyse biological membranes, may be a promising therapeutic agent in the treatment of cancer. However, because of its nonspecific actions, there is a need to use a delivery method. The conducted research determined whether carbon nanoparticles, such as graphene and graphene oxide, could be carriers for melittin to breast cancer cells. The studies included the analysis of intracellular pH, the potential of cell membranes, the type of cellular transport, and the expression of receptor proteins. By measuring the particle size, zeta potential, and FT-IT analysis, we found that the investigated nanoparticles are connected by electrostatic interactions. The level of melittin encapsulation with graphene was 86%, while with graphene oxide it was 78%. A decrease in pHi was observed for all cell lines after administration of melittin and its complex with graphene. The decrease in membrane polarization was demonstrated for all lines treated with melittin and its complex with graphene and after exposure to the complex of melittin with graphene oxide for the MDA-MB-231 and HFFF2 lines. The results showed that the investigated melittin complexes and the melittin itself act differently on different cell lines (MDA-MB-231 and MCF-7). It has been shown that in MDA-MD-231 cells, melittin in a complex with graphene is transported to cells via caveolin-dependent endocytosis. On the other hand, the melittin–graphene oxide complex can reach breast cancer cells through various types of transport. Other differences in protein expression changes were also observed for tumor lines after exposure to melittin and complexes.