Agentic AI systems have gained significant attention for their ability to autonomously perform complex tasks. However, their reliance on well-prepared tools limits their applicability in the medical domain, which requires to train specialized models. In this paper, we make three contributions: (i) We present M3Builder, a novel multi-agent system designed to automate machine learning (ML) in medical imaging. At its core, M3Builder employs four specialized agents that collaborate to tackle complex, multi-step medical ML workflows, from automated data processing and environment configuration to self-contained auto debugging and model training. These agents operate within a medical imaging ML workspace, a structured environment designed to provide agents with free-text descriptions of datasets, training codes, and interaction tools, enabling seamless communication and task execution. (ii) To evaluate progress in automated medical imaging ML, we propose M3Bench, a benchmark comprising four general tasks on 14 training datasets, across five anatomies and three imaging modalities, covering both 2D and 3D data. (iii) We experiment with seven state-of-the-art large language models serving as agent cores for our system, such as Claude series, GPT-4o, and DeepSeek-V3. Compared to existing ML agentic designs, M3Builder shows superior performance on completing ML tasks in medical imaging, achieving a 94.29% success rate using Claude-3.7-Sonnet as the agent core, showing huge potential towards fully automated machine learning in medical imaging.