In this paper, we determine the multi-hop route that maximizes the throughput between a given Device-to-Device (D2D) source-destination pair for delay sensitive applications. We solve the routing problem under per-link target rate and delay constraints, in addition to the stochastic interference constraint from the cellular network. We derive closed-form expressions for the achievable end-to-end throughput, delay and packet drop probability. Based on this analysis, we develop an optimal routing algorithm for throughput maximization. We confirm the accuracy of our analysis using Monte Carlo simulations and illustrate the tradeoff between delay and throughput. Further, we show that multi-hop route offers significant gains in end-to-end data rates compared to the direct link communication under the stochastic interference constraint imposed by the cellular network and the maximum delay constraint on the transmitted packets.