Inspired by the mechanism of acoustic–elastic metamaterial (AEMM) that exhibits a stop band gap for wave transmission, simultaneous vibration suppression and energy harvesting can be achieved by integrating AEMM with energy-harvesting component. This article presents an analytical study of a multifunctional system based on this concept. First, a mathematical model of a unit-cell AEMM embedded with a piezoelectric transducer is developed and analyzed. The most important finding is the double-valley phenomenon that can intensively widen the band gap under strong electromechanical coupling condition. Based on the mathematical model, a dimensionless parametric study is conducted to investigate how to tune the system to enhance its vibration suppression ability. Subsequently, a multicell system is conceptualized from the findings of the unit-cell system. In a similar way, dimensionless parametric studies are conducted to optimize the vibration suppression performance and the energy-harvesting performance severally. It turns out that different impedance matching schemes are required to achieve optimal vibration suppression and energy harvesting. To handle this problem, compromising solutions are proposed for weakly and strongly coupled systems, respectively. Finally, the characteristics of the AEMM-based piezoelectric energy harvester (PEH) from two functional aspects are summarized, providing several design guidelines in terms of system parameter tuning. It is concluded that certain tradeoff is required in the process of optimizing the performance toward dual functionalities.