The widespread adoption of Large Language Models (LLMs) has been hindered by their tendency to hallucinate, generating plausible but factually incorrect information. While Retrieval-Augmented Generation (RAG) systems attempt to address this issue by grounding responses in external knowledge, hallucination remains a persistent challenge, particularly for morphologically complex, low-resource languages like Turkish. This paper introduces Turk-LettuceDetect, the first suite of hallucination detection models specifically designed for Turkish RAG applications. Building on the LettuceDetect framework, we formulate hallucination detection as a token-level classification task and fine-tune three distinct encoder architectures: a Turkish-specific ModernBERT, TurkEmbed4STS, and multilingual EuroBERT. These models were trained on a machine-translated version of the RAGTruth benchmark dataset containing 17,790 instances across question answering, data-to-text generation, and summarization tasks. Our experimental results show that the ModernBERT-based model achieves an F1-score of 0.7266 on the complete test set, with particularly strong performance on structured tasks. The models maintain computational efficiency while supporting long contexts up to 8,192 tokens, making them suitable for real-time deployment. Comparative analysis reveals that while state-of-the-art LLMs demonstrate high recall, they suffer from low precision due to over-generation of hallucinated content, underscoring the necessity of specialized detection mechanisms. By releasing our models and translated dataset, this work addresses a critical gap in multilingual NLP and establishes a foundation for developing more reliable and trustworthy AI applications for Turkish and other languages.