This work proposes a unified Hierarchical Model Predictive Control (H-MPC) for modular manipulators across various morphologies, as the controller can adapt to different configurations to execute the given task without extensive parameter tuning in the controller. The H-MPC divides the control process into two levels: a high-level MPC and a low-level MPC. The high-level MPC predicts future states and provides trajectory information, while the low-level MPC refines control actions by updating the predictive model based on this high-level information. This hierarchical structure allows for the integration of kinematic constraints and ensures smooth joint-space trajectories, even near singular configurations. Moreover, the low-level MPC incorporates secondary linearization by leveraging predictive information from the high-level MPC, effectively capturing the second-order Taylor expansion information of the kinematic model while still maintaining a linearized model formulation. This approach not only preserves the simplicity of a linear control model but also enhances the accuracy of the kinematic representation, thereby improving overall control precision and reliability. To validate the effectiveness of the control policy, we conduct extensive evaluations across different manipulator morphologies and demonstrate the execution of pick-and-place tasks in real-world scenarios.