A Wireless Body Area Network (WBAN) is made up of multiple tiny physiological sensors implanted in/on the human body with each sensor equipped with a wireless transceiver that communicates to a coordinator in a star topology. Energy is the scarcest resource in WBANs. Power control mechanisms to achieve a certain level of utility while using as little power for transmission as possible can play an important role in reducing energy consumption in such very energy-constrained networks. In this paper, we propose a novel power controller to mitigate internetwork interference in WBANs and increase the maximum achievable throughput with the minimum energy consumption. The proposed power controller employs reinforcement learning with approximation to learn from the environment and improve its performance. We compare the performance of the proposed controller to two other power controllers, one based on game theory and the other one based on fuzzy logic. Simulation results show that compared to the other two approaches, RLPC provides a substantial saving in energy consumption per bit, with a substantial increase in network lifetime.