The photophysical behavior of a phenothiazine-phenyl-isoalloxazine dye dyad, a model system for blue-light photoreceptors functioning on the basis of photoinduced electron transfer, was investigated by employing a combination of time-dependent density functional and coupled-cluster response theory. A conical intersection between a "bright" locally excited and a "dark" charge-transfer state was found in the low-energy region of the corresponding potential energy surfaces. We propose that, for the solvated dyad, this conical intersection is responsible for the experimentally observed fast fluorescence quenching in that system.