Transdermal drug delivery (TDD) is an advantageous and effective approach for the localized delivery of drugs; however, overcoming the high impermeability of the outermost layer of skin, the stratum corneum, represents a significant challenge to TDD. Herein, we describe a simple and biocompatible platform based on a two-component molecular hydrogel for the transdermal delivery of the non-steroidal anti-inflammatory drug (S)-naproxen. The hydrogel is formed by two amphipathic tetrapeptides bearing aromatic side groups and oppositely-charged residues that co-assemble into fibrillar networks at pH 7.4. We demonstrate that (S)-naproxen, which possesses an aromatic region and an ionizable group, can be effectively loaded into the hydrogel. We characterized drug-loaded hydrogels by NMR and rheology and studied in vitro release under physiologically relevant conditions. Moreover, TDD studies on human skin samples demonstrated a twofold increase in the permeation of (S)-naproxen, which could be advantageous for the localized delivery of the drug.