Existing methods for enhancing the inductive reasoning of large language models (LLMs) at test-time typically depend on iterative self-refinement of hypotheses, which lacks explicit optimization guidance and effective error correction. This often results in superficial rewording and the accumulation of errors. To overcome these limitations, we propose MATSIR, a plug-and-play test-time framework integrating Multi-Agent coordination with Monte Carlo Tree Search to improve Inductive Reasoning. MATSIR incorporates a dual-reward mechanism that provides explicit refinement signals, promoting logically coherent and semantically enriched hypotheses rather than mere rephrasing. Furthermore, it enables trajectory-level error correction through backtracking and pruning, allowing the system to recover from erroneous intermediate hypotheses. Experiments on five benchmarks across four LLMs show that MATSIR consistently outperforms previous best methods, yielding the highest average improvement of +4.9% on QWQ-32B and all-round improvement on Deepseek-V3. Our findings highlight that explicit guided search with built-in error correction is essential for advancing inductive reasoning in LLMs. Code is available at https://github.com/SolarWindRider/MATSIR