The development of fluorescent proteins (FPs) has revolutionized cell biology research. The monomeric variants of red fluorescent proteins (RFPs), known as mFruits, have been especially valuable for tagging and tracking cellular processes in vivo. Determining oxygen diffusion pathways in FPs can be important for improving photostability and for understanding maturation of the chromophore. We use molecular dynamics (MD) calculations to investigate the diffusion of molecular oxygen in one of the most useful monomeric RFPs, mCherry. We describe a pathway that allows oxygen molecules to enter from the solvent and travel through the protein barrel to the chromophore. We calculate the free-energy of an oxygen molecule at points along the path. The pathway contains several oxygen hosting pockets, which are identified by the amino acid residues that form the pocket. We also investigate an RFP variant known to be significantly less photostable than mCherry and find much easier oxygen access in this variant. The results provide a better understanding of the mechanism of molecular oxygen access into the fully folded mCherry protein barrel and provide insight into the photobleaching process in these proteins.