Manipulating dynamic objects remains an open challenge for Vision-Language-Action (VLA) models, which, despite strong generalization in static manipulation, struggle in dynamic scenarios requiring rapid perception, temporal anticipation, and continuous control. We present DynamicVLA, a framework for dynamic object manipulation that integrates temporal reasoning and closed-loop adaptation through three key designs: 1) a compact 0.4B VLA using a convolutional vision encoder for spatially efficient, structurally faithful encoding, enabling fast multimodal inference; 2) Continuous Inference, enabling overlapping reasoning and execution for lower latency and timely adaptation to object motion; and 3) Latent-aware Action Streaming, which bridges the perception-execution gap by enforcing temporally aligned action execution. To fill the missing foundation of dynamic manipulation data, we introduce the Dynamic Object Manipulation (DOM) benchmark, built from scratch with an auto data collection pipeline that efficiently gathers 200K synthetic episodes across 2.8K scenes and 206 objects, and enables fast collection of 2K real-world episodes without teleoperation. Extensive evaluations demonstrate remarkable improvements in response speed, perception, and generalization, positioning DynamicVLA as a unified framework for general dynamic object manipulation across embodiments.