Large Language Models (LLMs) have shown significant promise in real-world decision-making tasks for embodied artificial intelligence, especially when fine-tuned to leverage their inherent common sense and reasoning abilities while being tailored to specific applications. However, this fine-tuning process introduces considerable safety and security vulnerabilities, especially in safety-critical cyber-physical systems. In this work, we propose the first comprehensive framework for Backdoor Attacks against LLM-based Decision-making systems (BALD) in embodied AI, systematically exploring the attack surfaces and trigger mechanisms. Specifically, we propose three distinct attack mechanisms: word injection, scenario manipulation, and knowledge injection, targeting various components in the LLM-based decision-making pipeline. We perform extensive experiments on representative LLMs (GPT-3.5, LLaMA2, PaLM2) in autonomous driving and home robot tasks, demonstrating the effectiveness and stealthiness of our backdoor triggers across various attack channels, with cases like vehicles accelerating toward obstacles and robots placing knives on beds. Our word and knowledge injection attacks achieve nearly 100% success rate across multiple models and datasets while requiring only limited access to the system. Our scenario manipulation attack yields success rates exceeding 65%, reaching up to 90%, and does not require any runtime system intrusion. We also assess the robustness of these attacks against defenses, revealing their resilience. Our findings highlight critical security vulnerabilities in embodied LLM systems and emphasize the urgent need for safeguarding these systems to mitigate potential risks.