We propose a novel task of text-controlled human object interaction generation in 3D scenes with movable objects. Existing human-scene interaction datasets suffer from insufficient interaction categories and typically only consider interactions with static objects (do not change object positions), and the collection of such datasets with movable objects is difficult and costly. To address this problem, we construct the InteractMove dataset for Movable Human-Object Interaction in 3D Scenes by aligning existing human object interaction data with scene contexts, featuring three key characteristics: 1) scenes containing multiple movable objects with text-controlled interaction specifications (including same-category distractors requiring spatial and 3D scene context understanding), 2) diverse object types and sizes with varied interaction patterns (one-hand, two-hand, etc.), and 3) physically plausible object manipulation trajectories. With the introduction of various movable objects, this task becomes more challenging, as the model needs to identify objects to be interacted with accurately, learn to interact with objects of different sizes and categories, and avoid collisions between movable objects and the scene. To tackle such challenges, we propose a novel pipeline solution. We first use 3D visual grounding models to identify the interaction object. Then, we propose a hand-object joint affordance learning to predict contact regions for different hand joints and object parts, enabling accurate grasping and manipulation of diverse objects. Finally, we optimize interactions with local-scene modeling and collision avoidance constraints, ensuring physically plausible motions and avoiding collisions between objects and the scene. Comprehensive experiments demonstrate our method's superiority in generating physically plausible, text-compliant interactions compared to existing approaches.