Ultra-Dense Network (UDN) deployment is considered a key element to achieve the requested capacity in future fifth-generation (5G) mobile networks. Backhaul networks in UDNs are formed by heterogeneous links with multi-hop connections and must handle massive traffic. Backhauling in future 5G networks may represent the capacity bottleneck. Therefore, there is the need for efficient and flexible routing schemes able to handle the dynamism of the traffic load in capacity-limited networks. Toward this goal, the emerging Software-Defined Network (SDN) paradigm provides an efficient solution, transferring the routing operation from the data plane switches to a central controller, thus achieving more flexibility, efficiency, and faster convergence time in comparison to conventional networks. This paper proposes and investigates an SDN-approach for an efficient routing in a capacity-limited backhaul network that carries data and control traffic of a heterogeneous UDN. The routing algorithm is centralized in the SDN controller and two different types of traffic flow are considered: data and control plane coordination traffic. The goal is to reduce or even to avoid the amount of traffic that the backhaul network is not able to support, distributing in a fair way the eventual lack of bandwidth among different access points. Simulation results show that with the considered approach the performance significantly improves, especially when there is an excess of traffic load in the network. Moreover, thanks to the SDN-based design, the network can reconfigure the traffic routing depending on the changing conditions.