Text-to-video (T2V) generative models have rapidly advanced and found widespread applications across fields like entertainment, education, and marketing. However, the adversarial vulnerabilities of these models remain rarely explored. We observe that in T2V generation tasks, the generated videos often contain substantial redundant information not explicitly specified in the text prompts, such as environmental elements, secondary objects, and additional details, providing opportunities for malicious attackers to embed hidden harmful content. Exploiting this inherent redundancy, we introduce BadVideo, the first backdoor attack framework tailored for T2V generation. Our attack focuses on designing target adversarial outputs through two key strategies: (1) Spatio-Temporal Composition, which combines different spatiotemporal features to encode malicious information; (2) Dynamic Element Transformation, which introduces transformations in redundant elements over time to convey malicious information. Based on these strategies, the attacker's malicious target seamlessly integrates with the user's textual instructions, providing high stealthiness. Moreover, by exploiting the temporal dimension of videos, our attack successfully evades traditional content moderation systems that primarily analyze spatial information within individual frames. Extensive experiments demonstrate that BadVideo achieves high attack success rates while preserving original semantics and maintaining excellent performance on clean inputs. Overall, our work reveals the adversarial vulnerability of T2V models, calling attention to potential risks and misuse. Our project page is at https://wrt2000.github.io/BadVideo2025/.