Multiphysics simulation frameworks such as MOOSE provide rigorous engines for phase-field materials modeling, yet adoption is constrained by the expertise required to construct valid input files, coordinate parameter sweeps, diagnose failures, and extract quantitative results. We introduce AutoMOOSE, an open-source agentic framework that orchestrates the full simulation lifecycle from a single natural-language prompt. AutoMOOSE deploys a five-agent pipeline in which the Input Writer coordinates six sub-agents and the Reviewer autonomously corrects runtime failures without user intervention. A modular plugin architecture enables new phase-field formulations without modifying the core framework, and a Model Context Protocol (MCP) server exposes the workflow as ten structured tools for interoperability with any MCP-compatible client. Validated on a four-temperature copper grain growth benchmark, AutoMOOSE generates MOOSE input files with 6 of 12 structural blocks matching a human expert reference exactly and 4 functionally equivalent, executes all runs in parallel with a 1.8x speedup, and performs an end-to-end physical consistency check spanning intent, finite-element execution, and Arrhenius kinetics with no human verification. Grain coarsening kinetics are recovered with R^2 = 0.90-0.95 at T >= 600 K; the recovered activation energy Q_fit = 0.296 eV is consistent with a human-written reference (Q_fit = 0.267 eV) under identical parameters. Three runtime failure classes were diagnosed and resolved autonomously within a single correction cycle, and every run produces a provenance record satisfying FAIR data principles. These results show that the gap between knowing the physics and executing a validated simulation campaign can be bridged by a lightweight multi-agent orchestration layer, providing a pathway toward AI-driven materials discovery and self-driving laboratories.