Agentic artificial intelligence (AI) presents a promising pathway toward realizing autonomous and self-improving wireless network services. However, resource-constrained, widely distributed, and data-heterogeneous nature of wireless networks poses significant challenges to existing agentic AI that relies on centralized architectures, leading to high communication overhead, privacy risks, and non-independent and identically distributed (non-IID) data. Federated learning (FL) has the potential to improve the overall loop of agentic AI through collaborative local learning and parameter sharing without exchanging raw data. This paper proposes new federated agentic AI approaches for wireless networks. We first summarize fundamentals of agentic AI and mainstream FL types. Then, we illustrate how each FL type can strengthen a specific component of agentic AI's loop. Moreover, we conduct a case study on using FRL to improve the performance of agentic AI's action decision in low-altitude wireless networks (LAWNs). Finally, we provide a conclusion and discuss future research directions.