The rapid advancement of Vision-Language Models (VLMs) has significantly advanced the development of Embodied Question Answering (EQA), enhancing agents' abilities in language understanding and reasoning within complex and realistic scenarios. However, EQA in real-world scenarios remains challenging, as human-posed questions often contain noise that can interfere with an agent's exploration and response, bringing challenges especially for language beginners and non-expert users. To address this, we introduce a NoisyEQA benchmark designed to evaluate an agent's ability to recognize and correct noisy questions. This benchmark introduces four common types of noise found in real-world applications: Latent Hallucination Noise, Memory Noise, Perception Noise, and Semantic Noise generated through an automated dataset creation framework. Additionally, we also propose a 'Self-Correction' prompting mechanism and a new evaluation metric to enhance and measure both noise detection capability and answer quality. Our comprehensive evaluation reveals that current EQA agents often struggle to detect noise in questions, leading to responses that frequently contain erroneous information. Through our Self-Correct Prompting mechanism, we can effectively improve the accuracy of agent answers.