Medical image segmentation is fundamental for biomedical discovery. Existing methods lack generalizability and demand extensive, time-consuming manual annotation for new clinical application. Here, we propose MedSAM-3, a text promptable medical segmentation model for medical image and video segmentation. By fine-tuning the Segment Anything Model (SAM) 3 architecture on medical images paired with semantic conceptual labels, our MedSAM-3 enables medical Promptable Concept Segmentation (PCS), allowing precise targeting of anatomical structures via open-vocabulary text descriptions rather than solely geometric prompts. We further introduce the MedSAM-3 Agent, a framework that integrates Multimodal Large Language Models (MLLMs) to perform complex reasoning and iterative refinement in an agent-in-the-loop workflow. Comprehensive experiments across diverse medical imaging modalities, including X-ray, MRI, Ultrasound, CT, and video, demonstrate that our approach significantly outperforms existing specialist and foundation models. We will release our code and model at https://github.com/Joey-S-Liu/MedSAM3.