Peptides have been thoroughly studied as new therapeutic strategies for cancer treatment. In this work, we explored in vitro the anticancer potential of three novel peptides derived from the C-terminal of azurin, an anticancer bacterial protein produced by Pseudomonas aeruginosa. CT-p26, CT-p19 and CT-p19LC peptides were previously obtained through an in silico peptide design optimization process, CT-p19LC being the most promising as it presented higher hydrophobicity and solubility, positive total charge and, most importantly, greater propensity for anticancer activity. Therefore, in this study, through proliferation and apoptosis assays, CT-p19LC was tested in four cancer cell lines—A549, MCF-7, HeLa and HT-29—and in two non-cancer cell lines—16HBE14o- and MCF10A. Its membrane-targeting activity was further evaluated with zeta potential measurements and membrane order was assessed with the Laurdan probe. The results obtained demonstrated that CT-p19LC decreases cell viability through induction of cell death and binds to the plasma membrane of cancer cells, but not to non-cancer cells, making them less rigid. Overall, this study reveals that CT-p19LC is an auspicious selective anticancer peptide able to react with cancer cell membranes and cause effective action.