Embodied Instruction Following (EIF) is the task of executing natural language instructions by navigating and interacting with objects in 3D environments. One of the primary challenges in EIF is compositional task planning, which is often addressed with supervised or in-context learning with labeled data. To this end, we introduce the Socratic Planner, the first zero-shot planning method that infers without the need for any training data. Socratic Planner first decomposes the instructions into substructural information of the task through self-questioning and answering, translating it into a high-level plan, i.e., a sequence of subgoals. Subgoals are executed sequentially, with our visually grounded re-planning mechanism adjusting plans dynamically through a dense visual feedback. We also introduce an evaluation metric of high-level plans, RelaxedHLP, for a more comprehensive evaluation. Experiments demonstrate the effectiveness of the Socratic Planner, achieving competitive performance on both zero-shot and few-shot task planning in the ALFRED benchmark, particularly excelling in tasks requiring higher-dimensional inference. Additionally, a precise adjustments in the plan were achieved by incorporating environmental visual information.