A linear dynamic network consists of a directed graph whose nodes are subsystems and whose arcs define dynamic couplings. Subsystem states evolve depending on the local and upstream control signals according to uncertain dynamics. Dynamic networks can serve as models for geographically distributed systems such as traffic networks and petrochemical plants. This technical note develops a distributed algorithm to operate a linear dynamic network with a network of agents that implement a distributed model predictive control strategy. Based on subgradient optimization to handle nondifferentiability, the distributed algorithm is shown to converge to an optimal solution.