Alzheimer’s disease (AD) is a neurodegenerative disorder marked by the progressive accumulation of amyloid-β (Aβ) plaques and tau protein tangles in the brain. These pathological aggregates interfere with neuronal function, leading to the disruption of cognitive processes, particularly memory. The deposition of Aβ forms senile plaques, while tau protein, in its hyperphosphorylated state, forms neurofibrillary tangles, both of which contribute to the underlying neurodegeneration observed in AD. Rosmarinic acid (RosA), a natural compound found in plants such as Rosmarinus officinalis, is known for its antioxidant, anti-inflammatory, and antimicrobial properties. Due to its ability to cross the blood–brain barrier, RosA holds promise as a nutritional supplement that may support brain health. In this study, molecular dynamics (MD) simulations were used to investigate the impact of RosA on the structural stability of Aβ peptides. The results indicated that the addition of RosA increased the instability of Aβ, as evidenced by an increase in the Root Mean Square Deviation (RMSD), a decrease in the Radius of Gyration (Rg), and an expansion of the Solvent Accessible Surface Area (SASA). This destabilization is primarily attributed to the disruption of native hydrogen bonds and hydrophobic interactions in the presence of two RosA molecules. The free energy landscape (FEL) analysis and MM-PBSA (Poisson-Boltzmann Surface Area Mechanics) results further support the notion that RosA can effectively bind to the hydrophobic pocket of the protein, highlighting its potential as a nutritional component that may contribute to maintaining brain health and function.