The distributed framework has been considered as one promising framework for the control of large-scale systems. In this work, we propose a coordination algorithm for distributed moving horizon state estimators (MHEs) for discrete-time linear systems composed of subsystems. In particular, the class of linear system we focus on is composed of several subsystems that interact with each other via their states. In the proposed coordinated distributed MHE (CDMHE) scheme, each subsystem is associated with a local MHE. In the design of a local MHE, a coordinating term is incorporated into its cost function which is determined by an upper-layer coordinator. At each sampling time, a local MHE estimates its local state and system noise, and then sends them to the coordinator. The coordinator calculates a price vector based on information received from all the local MHEs and sends the price vector together with the calculated interaction estimates to each local MHE. The above steps are performed iteratively every sampling time. It is shown that the CDMHE scheme is able to achieve the estimation performance of the corresponding centralized design if convergence at each sampling time is ensured. A simulation study based on a chemical process is presented to illustrate the applicability and effectiveness of the proposed scheme. The cases with communication failures, and premature termination are also discussed.