Embodied Agents are evolving from passive reasoning systems into active executors that interact with tools, robots, and physical environments. Once an agent gains execution authority, the central challenge shifts from how to make it act to how to keep its actions governable at runtime. Existing approaches embed safety, recovery, and decision constraints inside the agent loop, making execution control difficult to standardize, audit, and adapt across environments. We propose a runtime governance framework for policy-constrained execution that separates agent cognition from execution oversight. Governance is externalized into a dedicated runtime layer performing policy checking, capability admission, execution monitoring, rollback, and human override. We formalize the control boundary among a persistent Embodied Agent, modular Capability Packages, and the governance layer, and define a policy-constrained execution pipeline evaluated under controlled simulation. Over 1000 randomized trials, the framework achieves 96.2%+/-2.7% interception of unauthorized actions, reduces unsafe continuation from 100% to 22.2%+/-3.1% under runtime drift, and attains 90.7%+/-3.0% recovery success with full policy compliance. Comparison with five baselines, including AutoRT-style constitution filtering and RoboGuard-style two-stage guardrails, shows that pre-execution filtering is equally effective across governance-aware methods, while only the proposed framework provides continuous runtime detection (RVDR = 61.3% vs. 0%) and structured recovery (all p<0.001). A sensitivity sweep across the full detection range confirms a genuine detection-continuation trade-off. This work argues future embodied systems should be designed for governable execution.