In this paper, we introduce a distributed dynamic routing algorithm for secondary users (SUs) to minimize their interference with the primary users (PUs) in multi-hop cognitive radio (CR) networks. We use the medial axis with a relaxation factor as a reference path which is contingent on the states of the PUs. Along the axis, we construct a hierarchical structure for multiple sources to reach cognitive pilot channel (CPC) base stations. We use a temporal and spatial dynamic non-cooperative game to model the interactions among SUs as well as their influences from PUs in the multi-hop structure of the network. A multi-stage fictitious play learning is used for distributed routing in multi-hop CR networks. We obtain a set of mixed (behavioral) Nash equilibrium strategies of the dynamic game in closed form by backward induction. The proposed algorithm minimizes the overall interference and the average packet delay along the routing path from SU nodes to CPC base stations in an optimal and distributed manner.