Kubernetes has become the foundation of modern cloud-native infrastructure, yet its management remains complex and fragmented. Administrators must navigate a vast API surface, manage heterogeneous workloads, and coordinate tasks across disconnected tools - often requiring precise commands, YAML configuration, and contextual expertise. This paper presents KubeIntellect, a Large Language Model (LLM)-powered system for intelligent, end-to-end Kubernetes control. Unlike existing tools that focus on observability or static automation, KubeIntellect supports natural language interaction across the full spectrum of Kubernetes API operations, including read, write, delete, exec, access control, lifecycle, and advanced verbs. The system uses modular agents aligned with functional domains (e.g., logs, metrics, RBAC), orchestrated by a supervisor that interprets user queries, maintains workflow memory, invokes reusable tools, or synthesizes new ones via a secure Code Generator Agent. KubeIntellect integrates memory checkpoints, human-in-the-loop clarification, and dynamic task sequencing into a structured orchestration framework. Evaluation results show a 93% tool synthesis success rate and 100% reliability across 200 natural language queries, demonstrating the system's ability to operate efficiently under diverse workloads. An automated demo environment is provided on Azure, with additional support for local testing via kind. This work introduces a new class of interpretable, extensible, and LLM-driven systems for managing complex infrastructure.