This paper investigates energy efficiency maximization for movable antenna (MA)-aided multi-user uplink communication systems by considering the time delay and energy consumption incurred by practical antenna movement. We first examine the special case with a single user and propose an optimization algorithm based on the one-dimensional (1D) exhaustive search to maximize the user's energy efficiency. Moreover, we derive an upper bound on the energy efficiency and analyze the conditions required to achieve this performance bound under different numbers of channel paths. Then, for the general multi-user scenario, we propose an iterative algorithm to fairly maximize the minimum energy efficiency among all users. Simulation results demonstrate the effectiveness of the proposed scheme in improving energy efficiency compared to existing MA schemes that do not account for movement-related costs, as well as the conventional fixed-position antenna (FPA) scheme. In addition, the results show the robustness of the proposed scheme to imperfect channel state information (CSI) and provide valuable insights for practical system deployment.