Fog computing is a promising technology that can provide storage and computational services to future 6G networks. To support the massive Internet-of-Things (IoT) applications in 6G, fog computing will play a vital role. IoT devices and fog nodes have energy limitations and hence, energy-efficient techniques are needed for storage and computation services. We present an overview of massive IoT and 6G-enabling technologies. We discuss different energy-related challenges that arise while using fog computing in 6G-enabled massive IoT. We categorize different energy-efficient fog computing solutions for IoT and describe the recent work done in these categories. Finally, we discuss future opportunities and open challenges in designing energy-efficient techniques for fog computing in the future 6G massive IoT network.