Though the pharmacological activity of curcumin inhibiting the proliferation of certain cancer cells in culture was demonstrated, its effect on early-stage modifications induced in cell mechanics influencing hereby cell growth and cell adhesion are still questionable. We investigate the morphology and the elastic properties of live cultured, non-malignant human mammalian epithelial cells (HMEC) and cancerous breast epithelial cells (MCF7) by atomic force microscopy. We describe the different behavior of the two similar cell lines under curcumin treatment and we use fluorescence microscopy to identify the microtubules as the cytoskeleton structures responding to curcumin. The first changes in the HMEC cell morphology are observed after already 2 h incubation with curcumin. A 6-h long treatment leaves the MCF7 cells morphology non-affected, but the microtubules of HMEC cells disassemble and form a ring-like organization circumscribing the nuclear area. The observed morphological changes were correlated to modifications in cell's mechanics via elasticity force mapping measurements. Curcumin treatment modified elasticity of the HMEC cells increasing the cell's average Young's modulus two- to threefold, especially in the cytoplasmic area. Contrariwise, a slight decrease in the Young's modulus was noticed for the MCF7 cells, as they become softer due to the action of curcumin. Chemotherapeutic drugs exert their effect via the perturbation of the dynamic instability of the microtubule, hence the cell-specific perturbation induced by curcumin can help in future understanding of drug induced events on the cell behavior.