Aerial navigation is a fundamental yet underexplored capability in embodied intelligence, enabling agents to operate in large-scale, unstructured environments where traditional navigation paradigms fall short. However, most existing research follows the Vision-and-Language Navigation (VLN) paradigm, which heavily depends on sequential linguistic instructions, limiting its scalability and autonomy. To address this gap, we introduce UAV-ON, a benchmark for large-scale Object Goal Navigation (ObjectNav) by aerial agents in open-world environments, where agents operate based on high-level semantic goals without relying on detailed instructional guidance as in VLN. UAV-ON comprises 14 high-fidelity Unreal Engine environments with diverse semantic regions and complex spatial layouts, covering urban, natural, and mixed-use settings. It defines 1270 annotated target objects, each characterized by an instance-level instruction that encodes category, physical footprint, and visual descriptors, allowing grounded reasoning. These instructions serve as semantic goals, introducing realistic ambiguity and complex reasoning challenges for aerial agents. To evaluate the benchmark, we implement several baseline methods, including Aerial ObjectNav Agent (AOA), a modular policy that integrates instruction semantics with egocentric observations for long-horizon, goal-directed exploration. Empirical results show that all baselines struggle in this setting, highlighting the compounded challenges of aerial navigation and semantic goal grounding. UAV-ON aims to advance research on scalable UAV autonomy driven by semantic goal descriptions in complex real-world environments.