Click chemistry has been widely used for bioorthogonal labeling of biomolecules for its high efficiency, regioselectivity and biocompatibility. In this study, dansyl azide (DNS-AZ) was introduced as a novel fluorescence labeling reagent for the determination of alkynes based on copper (I)-catalyzed azide alkyne cycloaddition (CuAAC) click chemistry reaction. Rasagiline mesylate (RSM) is an irreversible, selective monoamine oxidase B (MAO-B) inhibitor. It is used as a model example for drugs with terminal alkyne moiety that could be monitored in biological samples with CuAAC reaction. RSM reacts with DNS-AZ in the presence of copper (II) and sodium ascorbate as catalysts to form stable 1,2,3-triazole derivative determined by HPLC with fluorescence detection. The developed methodology was optimized for sensitive and selective determination of RSM in rat plasma. Selegiline (SLG) was used as internal standard. The developed method was validated according to US-FDA guidelines in order to confirm method suitability for the intended application. The method allowed accurate and precise determination of RSM in the linearity range 0.50–100 ng mL−1 with a detection limit of 0.16 ng mL−1 for RSM in rat plasma. To confirm method applicability in real sample analysis, the developed method was employed to quantify RSM in a pharmacokinetic study in rats after administration of a single oral dose of RSM tablet.