Large language models (LLMs) with Mixture-of-Experts (MoE) architectures achieve impressive performance and efficiency by dynamically routing inputs to specialized subnetworks, known as experts. However, this sparse routing mechanism inherently exhibits task preferences due to expert specialization, introducing a new and underexplored vulnerability to backdoor attacks. In this work, we investigate the feasibility and effectiveness of injecting backdoors into MoE-based LLMs by exploiting their inherent expert routing preferences. We thus propose BadSwitch, a novel backdoor framework that integrates task-coupled dynamic trigger optimization with a sensitivity-guided Top-S expert tracing mechanism. Our approach jointly optimizes trigger embeddings during pretraining while identifying S most sensitive experts, subsequently constraining the Top-K gating mechanism to these targeted experts. Unlike traditional backdoor attacks that rely on superficial data poisoning or model editing, BadSwitch primarily embeds malicious triggers into expert routing paths with strong task affinity, enabling precise and stealthy model manipulation. Through comprehensive evaluations across three prominent MoE architectures (Switch Transformer, QwenMoE, and DeepSeekMoE), we demonstrate that BadSwitch can efficiently hijack pre-trained models with up to 100% success rate (ASR) while maintaining the highest clean accuracy (ACC) among all baselines. Furthermore, BadSwitch exhibits strong resilience against both text-level and model-level defense mechanisms, achieving 94.07% ASR and 87.18% ACC on the AGNews dataset. Our analysis of expert activation patterns reveals fundamental insights into MoE vulnerabilities. We anticipate this work will expose security risks in MoE systems and contribute to advancing AI safety.