Devices running on Wireless Sensor Networks (WSNs) generally have limited energy resources, which makes it important to design energy-aware algorithms. Capacitated Minimum Spanning Tree (CMST) algorithms can be designed for finding energy-aware routing paths and for load-balancing among sub-trees connected to the sink device. Despite being studied extensively in central settings, there has not been any energy-efficient algorithm for the WSNs. The bit complexity of applying a central approach in the sink node is O(n(2)logn) bits on a network having n nodes. In this work, we present the design of an algorithm which aims to solve CMST problem in WSNs and is based on Esau-Williams (E-W) algorithm. The bit complexity of the proposed algorithm is O(nlogn) bits. We compare the performance of the algorithm with the straightforward implementation of E-W where the problem is solved by the sink node and the result is sent to the other nodes. According to the computational results, our algorithm is more efficient than this version with respect to the energy consumption. Our algorithm (MCO) consumes up to 3 times less energy than central algorithm.