Humor generation is a challenging task in natural language generation that requires fluency, surprise, and cultural grounding. Although large language models (LLMs) show promise in English, little work addresses low-resource and culturally specific humor, such as in Korean. We propose **K-Humor**, a *dynamic multi-agent framework* for generating Korean jokes. Unlike static one-shot models, K-Humor integrates specialized agents for cultural awareness, audience simulation, editing, and punchline creation, which are coordinated through a dynamic iterative refinement loop. A human-data-grounded mechanism further guides the punchlines using authentic Korean jokes. Evaluation with automatic metrics, agent-internal diagnostics, LLM-as-a-judge, and human ratings shows that K-Humor consistently outperforms a single-prompt baseline and ablations in criteria such as fluency and cultural appropriateness. Although human-written jokes remain stronger overall, particularly on core creative dimensions, K-Humor demonstrates that dynamic, culturally grounded multi-agent systems can improve humor generation over standard LLM baselines in low-resource settings. Code is available at https://github.com/dxlabskku/k-humor.