The engineering of bacteriophytochrome photoreceptors into near-infrared fluorescent proteins is a promising route toward deep-tissue imaging of living cells with many challenges ahead. One key objective is to increase the fluorescence quantum yields, which are limited by competing non-radiative relaxation processes involving not only the well-known double-bond photoisomerization of the tetrapyrrole chromophore, but also a potential excited-state proton transfer from the chromophore to the protein. Motivated by the lack of mechanistic knowledge about this proton transfer, we here use hybrid quantum mechanics/molecular mechanics methods to investigate three possible scenarios for how the process is initiated. Through calculated excited-state pK_a values of the chromophore inside the protein matrix of Deinococcus radiodurans bacteriophytochrome, it is found that pyrrole ring C is a much more likely donor for excited-state proton transfer than rings A and B, which are also possible donors discussed in the literature. This finding offers a starting point for establishing a strategy to strengthen the fluorescence of engineered bacteriophytochromes through biochemical inhibition of the proton transfer.