Arabic document OCR remains a challenging task due to the language's cursive script, diverse fonts, diacritics, and right-to-left orientation. While modern Multimodal Large Language Models (MLLMs) have advanced document understanding for high-resource languages, their performance on Arabic remains limited. In this work, we introduce Baseer, a vision-language model fine-tuned specifically for Arabic document OCR. Leveraging a large-scale dataset combining synthetic and real-world documents, Baseer is trained using a decoder-only fine-tuning strategy to adapt a pre-trained MLLM while preserving general visual features. We also present Misraj-DocOCR, a high-quality, expert-verified benchmark designed for rigorous evaluation of Arabic OCR systems. Our experiments show that Baseer significantly outperforms existing open-source and commercial solutions, achieving a WER of 0.25 and establishing a new state-of-the-art in the domain of Arabic document OCR. Our results highlight the benefits of domain-specific adaptation of general-purpose MLLMs and establish a strong baseline for high-accuracy OCR on morphologically rich languages like Arabic.