The Z-source inverter (ZSI) is considered a suitable configuration for renewable energy systems due to its ability to provide both voltage step-up and step-down in a single stage. ZSI in renewable energy systems typically requires an appropriate closed-loop control strategy to ensure voltage regulation, grid connection, and maximum power point tracking (MPPT). Linear control strategies are generally formulated based on local linearization around a predefined operating point. Nevertheless, this approach does not guarantee the stability of a nonlinear system over a wide range of operating conditions. In this research, a novel multi-input multi-output (MIMO) Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) scheme is proposed for controlling the operation of a grid-connected single-phase ZSI. The dynamic behavior of the ZSI is modeled using the state-space averaging technique. Subsequently, the obtained averaged model is transformed into a port-controlled Hamiltonian (PCH) framework. The proposed IDA-PBC approach is capable of regulating all system state variables, including the grid-side AC current and the voltage across the DC-link capacitors. These states are regulated through the amplitude modulation index and the shoot-through duty cycle. Utilizing Lyapunov-based analysis, the asymptotic stability of the proposed control strategy is analytically verified. Furthermore, the controller achieves zero steady-state error in tracking both the DC-link reference voltage and the grid-injected AC reference current. The control design also demonstrates strong stability and robustness with respect to variations in system parameters. A series of simulations in MATLAB/Simulink have been conducted to assess the performance and robustness of the proposed control methodology.