This paper investigates an innovative movable antenna (MA)-enhanced multiple-input multiple-output (MIMO) system designed to enhance communication performance. We aim to maximize the energy efficiency (EE) under statistical channel state information (S-CSI) through a joint optimization of the transmit covariance matrix and the antenna position vectors (APVs). To solve the stochastic problem, we consider the large number of antennas scenario and resort to deterministic equivalent (DE) technology to reformulate the system EE w.r.t. the transmit variables, i.e., the transmit covariance matrix and APV, and the receive variables, i.e., the receive APV, respectively. Then, we propose an alternative optimization (AO) algorithm to update the transmit variables and the receive variables to maximize the system EE, respectively. Our numerical results reveal that, the proposed MA-enhanced system can significantly improve EE compared to several benchmark schemes and the optimal performance can be achieved with a finite size of movement regions for MAs.