Stimuli-responsive polymeric nanoparticles (NPs) can serve as smart drug delivery systems (DDSs) by triggering drug release upon external or internal stimuli. A dual-responsive DDS made of a triblock poly(ϵ-caprolactone)-poly(ethylene glycol)-poly(ϵ-caprolactone) (PCL-SS-PEG-SS-PCL) copolymer, bearing disulfide bonds between PCL and PEG, was synthesized. The copolymer was functionalized with coumarin and sensitive to near-infrared (NIR) light irradiation, while the S-S bonds could be cleaved by GSH (10 mM). Characterization was achieved by nuclear magnetic resonance, size exclusion chromatography, and Fourier transform infrared analyses. Nile Red (NR)-loaded NPs were prepared through self-assembly of the copolymer in water and analyzed by dynamic light scattering and field-emission scanning electron microscopy. The NR release upon ultraviolet (UV)/NIR light irradiation as well as by GSH concentrations was monitored by using fluorescence spectroscopy, while simultaneous exposure to UV/NIR light and intracellular GSH concentration led to faster NR release. AlamarBlue assay showed satisfactory cell viability of the NR-loaded NPs, while their cellular uptake in human dermal fibroblast cells was investigated by fluorescence microscopy and fluorescence emission measurements.