Mobile edge computing (MEC), which is an evolution of cloud computing, is acknowledged as a promising technology for meeting low latency and bandwidth efficiency required in fifth generation (5G) era. Accordingly, the enlargement of distributed MEC installments will be realized and their power consumption might be a significant problem in terms of operating costs for service providers. Thus, this paper proposes a theoretical framework for MEC server clustering to minimize power consumption of the MEC environment. To do this, considering power consumption behavior of MEC servers using CPUs with dynamic voltage frequency scaling, we propose a power-efficient clustering scheme (PECS) that minimizes power consumption of MEC servers by obtaining the optimal number of clusters through convex optimization. Numerical results reveal the proposed PECS reduces power consumption of the MEC environment by 12.32% relative to an existing scheme while sustaining average delay of inflows processed in MEC servers at the acceptable level without turning off MEC servers.