In donkeys, the use of frozen-thawed sperm for artificial insemination (AI) leads to low fertility rates. Furthermore, donkey sperm produce a large amount of reactive oxygen species (ROS), and post-AI inflammation induces the formation of neutrophil extracellular traps (NETosis), which further generates many more ROS. These high ROS levels may induce lipid peroxidation in the sperm plasma membrane, thus affecting its integrity. Enzymatic and non-enzymatic antioxidants, mainly found in the seminal plasma (SP), are responsible for maintaining the redox balance. However, this fluid is removed prior to cryopreservation, thereby exposing sperm cells to further oxidative stress. The exogenous addition of antioxidants to the freezing medium can reduce the detrimental effects caused by ROS generation. Therefore, the aim of this study was to evaluate how the addition of different reduced glutathione (GSH) concentrations (control, 2 mM, 4 mM, 6 mM, 8 mM, and 10 mM) to fresh sperm affect their cryotolerance. Total and progressive motility, kinematic parameters and motile sperm subpopulations were significantly (p < 0.05) different from the control in treatments containing 8 mM and 10 mM GSH, but not at lower concentrations. Plasma and acrosome membrane integrity, mitochondrial membrane potential (MMP) and intracellular superoxide levels (O2−) were not affected (p > 0.05) by any GSH concentration. Interestingly, however, the addition of 8 mM or 10 mM GSH reduced (p < 0.05) the percentages of viable sperm with high overall ROS levels compared to the control. In conclusion, frozen-thawed donkey sperm are able to tolerate high GSH concentrations, which differs from what has been observed in other species. This antioxidant capacity suggests that ROS could be important during post-AI and that the impact of using exogenous antioxidants like GSH to improve the sperm resilience to freeze-thawing is limited in this species.