Electric vehicles (EV) have gained importance in recent years due to environmental pollution and the future scarcity of fossil resources. They have been the subject of study for many years, where much work has focused on batteries and the electric motor (EM). There are several types of motors in the market but the most widely used are induction motors, especially squirrel cage motors. Induction motors have also been extensively studied and, nowadays, there are several control methods used—for example, those based on vector control, such as field-oriented control (FOC) and direct torque control (DTC). Further, at a higher level, such as the speed loop, several types of controllers, such as proportional integral (PI) and model predictive control (MPC), have been tested. This paper shows a comparison between a Continuous Control Set MPC (CCS-MPC) and a conventional PI controller within the FOC method, both in simulation and hardware in the loop (HIL) tests, to control the speed of an induction motor for an EV powered by lithium-ion batteries. The comparison is composed of experiments based on the speed and quality of response and the controllers’ stability. The results are shown graphically and numerically analyzed using performance metrics such as the integral of the absolute error (IAE), where the MPC shows a 50% improvement over the PI in the speed tracking performance. The efficiency of the MPC in battery consumption is also demonstrated, with 5.07 min more driving time.