Combining a vision module inside a closed-loop control system for a \emph{seamless movement} of a robot in a manipulation task is challenging due to the inconsistent update rates between utilized modules. This task is even more difficult in a dynamic environment, e.g., objects are moving. This paper presents a \emph{modular} zero-shot framework for language-driven manipulation of (dynamic) objects through a closed-loop control system with real-time trajectory replanning and an online 6D object pose localization. We segment an object within $\SI{0.5}{\second}$ by leveraging a vision language model via language commands. Then, guided by natural language commands, a closed-loop system, including a unified pose estimation and tracking and online trajectory planning, is utilized to continuously track this object and compute the optimal trajectory in real-time. Our proposed zero-shot framework provides a smooth trajectory that avoids jerky movements and ensures the robot can grasp a non-stationary object. Experiment results exhibit the real-time capability of the proposed zero-shot modular framework for the trajectory optimization module to accurately and efficiently grasp moving objects, i.e., up to \SI{30}{\hertz} update rates for the online 6D pose localization module and \SI{10}{\hertz} update rates for the receding-horizon trajectory optimization. These advantages highlight the modular framework's potential applications in robotics and human-robot interaction; see the video in https://www.acin.tuwien.ac.at/en/6e64/.