The study of Distributed Model Predictive Control (DMPC) for dynamically coupled linear systems has so far typically focused on situations where coupling constraints between subsystems are absent. In order to address the presence of convex coupling constraints, we present a distributed version of Han’s parallel algorithm for a class of convex programs. The distributed algorithm relies on local iterative updates only, instead of system-wide information exchange as in Han’s parallel algorithm. The new algorithm then provides the basis for a distributed MPC method that is applicable to sparsely coupled linear dynamical systems with coupled linear constraints. Convergence to the global optimum, recursive feasibility, and stability are established using only local communications between the subsystems.