DNA-based fluorescent Ag clusters attract much attention due to their high brightness and sensitivity to environment, which can be used in chemical sensing and biosensing applications. Low chemical yield of the fluorescent Ag clusters in solution hinders measuring of their absorption cross-section in the ground state and rate constants in the excited states. We applied fluorescence saturation spectroscopy for determining the photophysical constants of an oligonucleotide-stabilized red emitting Ag cluster. Power dependencies of the fluorescence response to the pulse excitation with different pulse duration allowed us to obtain the values of absorption cross-section, dark states formation and deactivation rates of the cluster. The Ag fluorescent cluster exhibited a relatively high (17%) efficiency of a long-lived dark state formation. This feature of the Ag cluster might be further interesting for possible photodynamic and microscopy applications.