Cisplatin (CP) is a well-known chemotherapeutic drug that displays dose-limiting nephrotoxicity. In this study, tannic acid (TA), a naturally occurring plant polyphenol, was evaluated for its antioxidant and antigenotoxicity potential against the CP-induced renal oxidative stress and genotoxicity in Swiss albino mice. The mice were given a prophylactic treatment of TA orally at a dose of 40 and 80 mg/kg body weight (b wt) for 7 consecutive days before the administration of a single intraperitoneal (i.p.) injection of CP at 7 mg/kg b wt. The modulatory effects of TA on CP-induced nephrotoxicity and genotoxicity were investigated by assaying oxidative stress biomarkers, serum kidney toxicity markers, DNA fragmentation, alkaline unwinding, micronuclei assay, and by histopathological examination of kidney architecture. CP administration altered the antioxidant levels, enhanced lipid peroxidation, induced DNA strand breaks, and altered the levels of micronuclei among polychromatic erythrocytes (PCEs) significantly (p < 0.001). Pretreatment of TA in mice showed significant (p < 0.001) recovery in antioxidant status, viz., reduced glutathione content and its dependent enzymes, quinone reductase and γ-glutamyl transpeptidase. TA significantly (p < 0.001) reinstated the normal serum levels of blood urea nitrogen (BUN) and creatinine. TA showed strongly inhibited (p < 0.001) micronuclei induction, DNA strand breaks, and DNA fragmentation. Thus, TA as a phytochemical protects kidneys through its antigenotoxic activity and antioxidant potential.