In this study, we examined the impact of hydrated fullerene C60 FWS on biochemical and morphological characteristics of Crassostrea gigas oysters during hypothermic storage. The study employed 10−4 M hydrated fullerene C60FWS. The experimental group (EG) samples were immersed in fullerene C60 FWS-containing seawater solution (10−8 M) for 24 h. The control group (CG) samples were exposed to similar conditions but without fullerene C60 FWS. In the EG samples, on day 4 of storage, no significant changes were noted in the studied parameters compared to the previous timepoint (day 1). Simultaneously, in the CG, there was an increase in the total protein (TP) concentration of by 17.3% and a decrease in the (lactate dehydrogenase) LDH activity by 12.3%, γ-glutamyltransferase (ɣGGT) activity by 21.8%, glucose-6-phosphate dehydrogenase (G6PDH) activity by 14.5%, and the total metabolic activity by 9.1% relative to the baseline (p < 0.05). On day 8 of storage, these changes were more evident in the CG, viz.: a 17.3% increase in the TP content, a 31.5% decrease in the LDH activity, a 37.4% decrease in the ɣGGT activity, a 18.2% decrease in the G6PDH activity, and a 25.2% decrease in the total metabolic activity compared to the EG (p < 0.05). In addition, on day 8, dystrophy and undulating degeneration were observed in the muscle tissue of oysters in the CG. Rare foci of muscle tissue dystrophy were found in EG samples. Therefore, fullerene C60 FWS used for hypothermic storage of oysters prevents and mitigates ischemic-reperfusion pathological processes in mollusk tissues that occur during hypothermic storage.