In the future Internet of Things (IoT), battery-powered devices equipped with short range radios may need to communicate with each other over multi-hop links. This may significantly increase their energy consumption. Whereas most research on IoT assumes that the devices use energy-efficient IEEE 802.15.4 wireless transceivers, we focus on IEEE 802.11 because of its wide penetration in consumer electronics such as toys. We extend the IEEE 802.11 power saving mode (PSM), which allows the devices to enter the low-power doze state, with a traffic announcement scheme that facilitates multi-hop communication. The scheme propagates traffic announcements along multi-hop paths to ensure that all intermediate nodes remain awake to forward the pending data frames with minimum latency. Simulation results show that the proposed Multi-Hop PSM (MH-PSM) improves both end-to-end delay and doze time compared to the standard PSM. MH-PSM is practical and software-implement able since it does not require changes to the parts of the IEEE 802.11 medium access control that are typically implemented in hardware.