Robotic search of people in human-centered environments, including healthcare settings, is challenging as autonomous robots need to locate people without complete or any prior knowledge of their schedules, plans or locations. Furthermore, robots need to be able to adapt to real-time events that can influence a person's plan in an environment. In this paper, we present MLLM-Search, a novel zero-shot person search architecture that leverages multimodal large language models (MLLM) to address the mobile robot problem of searching for a person under event-driven scenarios with varying user schedules. Our approach introduces a novel visual prompting method to provide robots with spatial understanding of the environment by generating a spatially grounded waypoint map, representing navigable waypoints by a topological graph and regions by semantic labels. This is incorporated into a MLLM with a region planner that selects the next search region based on the semantic relevance to the search scenario, and a waypoint planner which generates a search path by considering the semantically relevant objects and the local spatial context through our unique spatial chain-of-thought prompting approach. Extensive 3D photorealistic experiments were conducted to validate the performance of MLLM-Search in searching for a person with a changing schedule in different environments. An ablation study was also conducted to validate the main design choices of MLLM-Search. Furthermore, a comparison study with state-of-the art search methods demonstrated that MLLM-Search outperforms existing methods with respect to search efficiency. Real-world experiments with a mobile robot in a multi-room floor of a building showed that MLLM-Search was able to generalize to finding a person in a new unseen environment.