Traditional routing protocols employ limited information to make routing decisions, which leads to slow adaptation to traffic variability and restricted support to the quality of service requirements of applications. To address these shortcomings, in previous work, we proposed RSIR, a routing solution based on Reinforcement Learning (RL) in Software-Defined Networking (SDN). However, RL-based solutions usually suffer an increase in time during the learning process when dealing with large action and state spaces. This paper introduces a different routing approach, called Deep Reinforcement Learning and Software-Defined Networking Intelligent Routing (DRSIR). DRSIR defines a routing algorithm based on Deep RL (DRL) in SDN that overcomes the limitations of RL-based solutions. DRSIR considers path-state metrics to produce proactive, efficient, and intelligent routing that adapts to dynamic traffic changes. DRSIR was evaluated by emulation using real and synthetic traffic matrices. The results show that this solution outperforms the routing algorithms based on Dijkstra's algorithm and RSIR in relation to stretch, packet loss, and delay. Moreover, the results obtained demonstrate that DRSIR provides a practical and feasible solution for routing in SDN.