Large Language Models have shown remarkable potential as autonomous agents, but their effectiveness in knowledge-intensive tasks remains limited by passive knowledge utilization. We introduce KARL (Knowledge-Augmented Reinforcement Learning), a framework that enables LLM agents to dynamically explore structured knowledge sources through multi-turn interactions. Unlike existing retrieval-augmented approaches, KARL empowers agents to proactively decide when and what knowledge to acquire during task execution. Our framework incorporates online reinforcement learning with curiosity-driven reward shaping, explicitly incentivizing knowledge exploration while optimizing tool-use behaviors end-to-end. Extensive evaluation across six structured knowledge benchmarks demonstrates that KARL achieves state-of-the-art performance, with our Qwen2.5-14B-based agent significantly outperforming GPT-4o, Claude-4, and o4-mini on both knowledge graph and database tasks.Source code is available at https://github.com/THUDM/KARL.