Wormhole routing has been widely used in practical systems such as iWarp and Ncube-2. To avoid potential deadlock, a physical network can be partitioned into several virtual networks to break possible cyclic dependencies. An n-dimensional mesh can be partitioned into 2^n-l virtual networks and, if messages are always routed through paths with shortest Manhattan distance, deadlock can be avoided. This paper studies the problem of finding low congestion deadlock free routing on mesh connected multiprocessors which support virtual networks. We show that finding such a minimal maximum congestion routing for an arbitrary set of messages is NP-hard for an n dimensional mesh (n > 2). An efficient heuristic is proposed and performance of the heuristic is evaluated.