Site-selective dissociation induced by core photoexcitation of biomolecules is of key importance for the understanding of radiation damage processes and dynamics and for its promising use as "chemical scissors" in various applications. However, identifying products of site-selective dissociation in large molecules is challenging at the carbon, nitrogen, and oxygen edges because of the high recurrence of these atoms and related chemical groups. In this paper, we present the observation of site-selective dissociation at the sulfur L-edge in the gas-phase peptide methionine enkephalin, which contains only a single sulfur atom. Near-edge X-ray absorption mass spectrometry has revealed that the resonant S 2p → σ*C-S excitation of the sulfur contained in the methionine side chain leads to site-selective dissociation, which is not the case after core ionization above the sulfur L-edge. The prospects of such results for the study of charge dynamics in biomolecular systems are discussed.