Multi-agent systems (MAS) powered by Large Language Models (LLMs) have been demonstrated to push the boundaries of LLM capabilities, yet they often incur significant costs and face challenges in dynamic LLM selection. Current LLM routing methods effectively reduce overhead in single-agent scenarios by customizing LLM selection for each query, but they overlook the critical decisions regarding collaboration modes and agent roles in MAS. In response to this challenge, we first introduce the problem of Multi-Agent System Routing (MASR), which integrates all components of MAS into a unified routing framework. Toward this goal, we propose MasRouter, the first high-performing, cost-effective, and inductive MASR solution. MasRouter employs collaboration mode determination, role allocation, and LLM routing through a cascaded controller network, progressively constructing a MAS that balances effectiveness and efficiency. Extensive experiments demonstrate that MasRouter is (1) high-performing, achieving a $1.8\%\sim8.2\%$ improvement over the state-of-the-art method on MBPP; (2) economical, reducing overhead by up to $52.07\%$ compared to SOTA methods on HumanEval; and (3) plug-and-play, seamlessly integrating with mainstream MAS frameworks, reducing overhead by $17.21\%\sim28.17\%$ via customized routing. The code is available at https://github.com/yanweiyue/masrouter.