Experimental and epidemiological studies have shown that the nonsteroidal antiinflammatory drug naproxen may be useful in the treatment of Alzheimer's disease. To investigate the interactions of naproxen with Aβ dimers, which are the smallest cytotoxic aggregated Aβ peptide species, we use united atom implicit solvent model and exhaustive replica exchange molecular dynamics. We show that naproxen ligands bind to Aβ dimer and penetrate its volume interfering with the interpeptide interactions. As a result naproxen induces a destabilizing effect on Aβ dimer. By comparing the free-energy landscapes of naproxen interactions with Aβ dimers and fibrils, we conclude that this ligand has stronger antiaggregation potential against Aβ fibrils rather than against dimers. The analysis of naproxen binding energetics shows that the location of ligand binding sites in Aβ dimer is dictated by the Aβ amino acid sequence. Comparison of the in silico findings with experimental observations reveals potential limitations of naproxen as an effective therapeutic agent in the treatment of Alzheimer's disease.