A method for measuring the concentration of exosomes in biological objects using selective fluorescence labeling followed by nonselective enhancement by plasmonic nanoparticles is suggested. Theoretical investigation of the suggested approach is conducted. A model for description of the interaction of the incident wave, fluorophore, and plasmonic nanoparticles is developed. Calculations of the fluorescence enhancement of the molecule in the vicinity of the gold or silver nanoparticles are conducted with consideration of the actual dispersion of dielectric permittivity of metals. The physical mechanisms of the fluorescence enhancement—change of the local field in the vicinity of nanoparticles, difference in the radiation efficiency of the fluorophore and nanoparticle, and superradiance—are analyzed.