Using all-atom explicit water model and replica exchange molecular dynamics, we study the interactions between Aβ monomer and nonsteroidal anti-inflammatory drug ibuprofen, which is known to reduce the risk of Alzheimer's disease. Ibuprofen binding to Aβ is largely governed by hydrophobic effect, and its binding site in Aβ peptide is entirely composed of hydrophobic amino acids. Electrostatic interactions between negatively charged ibuprofen ligands and positively charged side chains make a relatively small contribution to binding. This outcome is explained by the competition of ligand-peptide electrostatic interactions with intrapeptide salt bridges. Consistent with the experiments, the S-isomer of ibuprofen binds with stronger affinity to Aβ than the R-isomer. Conformational ensemble of Aβ monomer in ibuprofen solution reveals two structured regions, 19-25 (R1) and 29-35 (R2), composed of turn/helix and helix structure, respectively. The clustering technique and free energy analysis suggest that Aβ conformational ensemble is mainly determined by the formation of Asp23-Lys28 salt bridge and the hydrophobic interactions between R1 and R2. Control simulations of Aβ peptide in ligand-free water show that ibuprofen binding changes Aβ structure by promoting the formation of helix and Asp23-Lys28 salt bridge. Implications of our findings for Aβ amyloidogenesis are discussed.