When an ad hoc network with limited link capacities is used to transport high-rate, latency-constrained multimedia streams, it is important that routing algorithms not only yield high aggregated bandwidth, but also minimize network congestion to avoid excessive delay. We propose a distributed algorithm to achieve congestion-minimized multi-path routing. The optimal solution can be approximated by decomposing the total target rate into a sequence of rate increments, and using the classical Bellman-Ford algorithm to find a corresponding minimum-cost route for each increment. Simulation results for video streaming over an ad hoc network show that compared to a centralized scheme, the approximations introduced by the distributed algorithm lead to performance loss of less than 0.5 dB in PSNR of received video quality.