This study aims to prepare a novel breast cancer-targeted micelle-based nanocarrier, which is stable in circulation, allowing intracellular drug release, and to investigate its cytotoxicity, apoptosis, and cytostatic effects, in vitro. The shell part of the micelle is composed of zwitterionic sulfobetaine ((N-3-sulfopropyl-N,N-dimethylamonium)ethyl methacrylate), while the core part is formed by another block, consisting of AEMA (2-aminoethyl methacrylamide), DEGMA (di(ethylene glycol) methyl ether methacrylate), and a vinyl-functionalized, acid-sensitive cross-linker. Following this, a targeting agent (peptide (LTVSPWY) and antibody (Herceptin®)), in varying amounts, were coupled to the micelles, and they were characterized by 1H NMR, FTIR (Fourier-transform infrared spectroscopy), Zetasizer, BCA protein assay, and fluorescence spectrophotometer. The cytotoxic, cytostatic, apoptotic, and genotoxic effects of doxorubicin-loaded micelles were investigated on SKBR-3 (human epidermal growth factor receptor 2 (HER2)-positive) and MCF10-A (HER2-negative). According to the results, peptide-carrying micelles showed a higher targeting efficiency and better cytostatic, apoptotic, and genotoxic activities than antibody-carrying and non-targeted micelles. Also, micelles masked the toxicity of naked DOX on healthy cells. In conclusion, this nanocarrier system has great potential to be used in different drug-targeting strategies, by changing targeting agents and drugs.