Abstract We examine spatial variations of the C0$/$CO abundance ratio (XC/CO) in the vicinity of the γ-ray supernova remnant W 51 C, based on [C i] (3P1–3P0), 12CO(1–0), and 13CO(1–0) observations with the ASTE and Nobeyama 45 m telescopes. We find that XC/CO varies in a range of 0.02–0.16 (0.05 in median) inside the molecular clouds of AV > 100 mag, where photodissociation of CO by the interstellar UV is negligible. Furthermore, XC/CO is locally enhanced by a factor of up to four near the W 51 C center, depending on the projected distance from the W 51 C center. In high-AV molecular clouds, XC/CO is determined by the ratio of the cosmic-ray (CR) ionization rate to the H2 density, and we find no clear spatial variation of the H2 density against the projected distance. Hence, the high CR ionization rate may locally enhance XC/CO near the W 51 C center. We also find that the observed spatial extent of the enhanced XC/CO (∼17 pc) is consistent with the diffusion distance of CRs with an energy of 100 MeV. This fact suggests that the low-energy CRs accelerated in W 51 C enhance XC/CO. The CR ionization rate in the XC/CO-enhanced cloud is estimated to be 3 × 10−16 s−1 on the basis of time-dependent photodissociation region simulations of XC/CO, the value of which is 30 times higher than that in the standard Galactic environment. These results demonstrate that [C i] is a powerful probe to investigate the interaction between CRs and the interstellar medium for a wide area in the vicinity of supernova remnants.