Interactive Object Grasping (IOG) is the task of identifying and grasping the desired object via human-robot natural language interaction. Current IOG systems assume that a human user initially specifies the target object's category (e.g., bottle). Inspired by pragmatics, where humans often convey their intentions by relying on context to achieve goals, we introduce a new IOG task, Pragmatic-IOG, and the corresponding dataset, Intention-oriented Multi-modal Dialogue (IM-Dial). In our proposed task scenario, an intention-oriented utterance (e.g., "I am thirsty") is initially given to the robot. The robot should then identify the target object by interacting with a human user. Based on the task setup, we propose a new robotic system that can interpret the user's intention and pick up the target object, Pragmatic Object Grasping (PROGrasp). PROGrasp performs Pragmatic-IOG by incorporating modules for visual grounding, question asking, object grasping, and most importantly, answer interpretation for pragmatic inference. Experimental results show that PROGrasp is effective in offline (i.e., target object discovery) and online (i.e., IOG with a physical robot arm) settings.