Cryopreservation of goat spermatozoa is challenging due to several factors, including one of the most essential, i.e., oxidative stress. It is particularly essential in goat semen due to its scanty ejaculate volume and high sperm concentration. This leaves a narrow sperm-to-seminal plasma ratio owing to marginal antioxidant support; moreover, semen extension further dilutes the antioxidant level, leading to an imbalance of oxidant-antioxidant equilibrium. The present study aimed to evaluate the effect of quercetin on curtailing oxidative stress and its reflection on the post-thaw survivability and membrane integrity of goat spermatozoa. For this study, six bucks were selected. Six ejaculates from each buck totaling 36 ejaculates were collected, which were then split into five parts; furthermore, each part was added with a semen extender having a particular concentration of additive. Group C without quercetin and T1 containing Vitamin E at 3 mmol/mL were considered the control and positive control respectively, whereas T2, T3, and T4 contain 10, 20, and 30 μmol/mL of Quercetin respectively. The final sperm concentration of each group was kept at 200 × 106 spermatozoa/mL. All groups were subjected to equilibration at 4 °C for 4 h, then filled in French mini (0.25 mL) straws, followed by sealing and cryopreservation. Samples after 72 h of cryopreservation were subjected to evaluation of plasma membrane integrity and viability through staining, acrosomal integrity, and mitochondrial membrane activity through flow cytometry. Evaluation of sperm kinematics as well as the oxidant-antioxidant status of sperm (ROS and nitric oxide) and seminal plasma (SOD, CAT, GPx, FRAP, and lipid peroxidation through MDA estimation) were also carried out. Quercetin, when supplemented at 20 μmol/mL in buck semen extender, significantly (p < 0.01) improved cryopreserved sperm functions in terms of plasma membrane integrity, viability, acrosomal integrity, mitochondrial membrane activity, and sperm kinematics of buck semen. Similarly, Quercetin supplementation at 20 μmol/mL significantly reduced reactive oxygen and nitrogen species (RONS) in sperm and improved the antioxidant status of seminal plasma, which was indicated by reduced oxidative damage and improved the antioxidant status of buck semen. In conclusion, Quercetin at 20 μmol/mL reduced oxidative stress, improved semen antioxidant status, and improved sperm membranes integrity and kinematics.