Wireless Body Area Networks (WBANs) are an emerging technology for short-range wireless communication inside, on or around the human body, mainly for medical applications. A WBAN's scarcest resource is power. Due to the mobility of WBANs as well as the limited number of available channels, signals of neighboring WBANs can cause interference that may severely degrade the reliability and performance of the system and lead to more power consumption. In this paper, we propose a fast converging fuzzy power controller (FPC) with feedback whose inputs are the current interference power level, Signal-to-Interference-and-Noise (SINR) and the current transmission power level to provide interference mitigation in WBANs. We utilize a genetic algorithm to design and optimize the FPC to simultaneously maximize capacity, minimize power consumption and minimize convergence time. We compare the performance of the proposed approach with two game-theory power control approaches. Our simulation results show that compared to these other approaches, the proposed FPC provides a substantial saving in power consumption as well as quick convergence that is independent of the number of nodes in the system, while sacrificing only a small amount of capacity.