Prompt relevance is a critical yet underexplored dimension in Arabic Automated Essay Scoring (AES). We present the first systematic study of binary prompt-essay relevance classification, supporting both AES scoring and dataset annotation. To address data scarcity, we built a synthetic dataset of on-topic and off-topic pairs and evaluated multiple models, including threshold-based classifiers, SVMs, causal LLMs, and a fine-tuned masked SBERT model. For real-data evaluation, we combined QAES with ZAEBUC, creating off-topic pairs via mismatched prompts. We also tested prompt expansion strategies using AraVec, CAMeL, and GPT-4o. Our fine-tuned SBERT achieved 98% F1 on synthetic data and strong results on QAES+ZAEBUC, outperforming SVMs and threshold-based baselines and offering a resource-efficient alternative to LLMs. This work establishes the first benchmark for Arabic prompt relevance and provides practical strategies for low-resource AES.