Time-resolved and steady-state emission techniques were employed to study the fluorescence quenching by excess protons of the electrically neutral compound riboflavin in methanol-doped ice samples. We found a very large fluorescence quenching effect by excess protons. This phenomenon has also been observed previously for the negatively charged flavin mononucleotide (FMN) in ice. We assume that the fluorescence quenching rate-determining step is the proton diffusion in the bulk ice. The diffusion-controlled rate constant in recombination reactions for charged molecules depends on the dielectric constant of the medium, whereas for neutral molecules it does not. The theory of the electric properties of ice argues that the dielectric constant depends strongly on the ice doping, and thus the extracted value of the diffusion constant depends on the actual value of the dielectric constant, which was ambiguous in our previous experiments. The current experiments on neutral molecules confirm previous studies based on charged molecules, showing that the proton diffusion constant in methanol-doped ice in the temperature range of 242-262 K is about 10 times that of water at 295 K.