Nowadays, increasing digitization may give acoustic communication an essential role in areas where electromagnetic communication cannot be employed, or only with extensive effort. Consequently, challenges from real-world applications are increasingly important for the deployment of acoustic communication systems. One major challenge to be addressed is the limited energy resources that battery-powered sensor nodes possess. Besides the high energy consumption during transmission and reception, listening to the communication channel for synchronization between transmitter and receiver is a major energy consuming factor. For this purpose, we introduce the concept of wake-up receivers known from radio technology for acoustic communication systems. Therefore, in this contribution a concept of a low-power acoustic wake-up receiver is presented and implemented with a demonstrator through a 1.6 mm thick metal barrier. We exploit the thickness vibration mode of a piezoelectric transducer at 1.2 MHz to form a subcarrier at 18 kHz. A selective wake-up with a 16 bit address is generated at a data rate of 1 kbps. The acoustic wake-up receiver reliably detects a valid wake-up at an energy consumption of 15 µW.