Semantic reasoning and dynamic planning capabilities are crucial for an autonomous agent to perform complex navigation tasks in unknown environments. It requires a large amount of common-sense knowledge, that humans possess, to succeed in these tasks. We present SayNav, a new approach that leverages human knowledge from Large Language Models (LLMs) for efficient generalization to complex navigation tasks in unknown large-scale environments. SayNav uses a novel grounding mechanism, that incrementally builds a 3D scene graph of the explored environment as inputs to LLMs, for generating feasible and contextually appropriate high-level plans for navigation. The LLM-generated plan is then executed by a pre-trained low-level planner, that treats each planned step as a short-distance point-goal navigation sub-task. SayNav dynamically generates step-by-step instructions during navigation and continuously refines future steps based on newly perceived information. We evaluate SayNav on a new multi-object navigation task, that requires the agent to utilize a massive amount of human knowledge to efficiently search multiple different objects in an unknown environment. SayNav outperforms an oracle based Point-nav baseline, achieving a success rate of 95.35% (vs 56.06% for the baseline), under the ideal settings on this task, highlighting its ability to generate dynamic plans for successfully locating objects in large-scale new environments. In addition, SayNav also enables efficient generalization of learning to navigate from simulation to real novel environments.