Curcumin (CUR) has potent anticancer activities, and its bioformulations, including biodegradable polymers, are increasingly able to improve CUR’s solubility, stability, and delivery to cancer cells. In this study, copolymers comprising poly (L-lactide)-poly (ethylene glycol)-poly (L-lactide) (PLA-PEG-PLA) and poly (ethylene glycol)-poly (L-lactide)-poly (ethylene glycol) (PEG-PLA-PEG) were designed and synthesized to assess and compare their CUR-delivery capacity and inhibitory potency on MCF-7 breast cancer cells. Molecular dynamics simulations and free energy analysis indicated that PLA-PEG-PLA has a higher propensity to interact with the cell membrane and more negative free energy, suggesting it is the better carrier for cell membrane penetration. To characterize the copolymer synthesis, Fourier transform-infrared (FT-IR) and proton nuclear magnetic resonance (1H-NMR) were employed, copolymer size was measured using dynamic light scattering (DLS), and their surface charge was determined by zeta potential analysis. Characterization indicated that the ring-opening polymerization (ROP) reaction was optimal for synthesizing high-quality polymers. Microspheres comprising the copolymers were then synthesized successfully. Of the two formulations, PLA-PEG-PLA experimentally exhibited better results, with an initial burst release of 17.5%, followed by a slow, constant release of the encapsulated drug up to 80%. PLA-PEG-PLA-CUR showed a significant increase in cell death in MCF-7 cancer cells (IC50 = 23.01 ± 0.85 µM) based on the MTT assay. These data were consistent with gene expression studies of Bax, Bcl2, and hTERT, which showed that PLA-PEG-PLA-CUR induced apoptosis more efficiently in these cells. Through the integration of nano-informatics and in vitro approaches, our study determined that PLA-PEG-PLA-CUR is an optimal system for delivering curcumin to inhibit cancer cells.