In recent years, computer networks and telecommunications in general have been shifting paradigms to adopt software-centric approaches. Software Defined Networking (SDN) is one of such paradigms that centralizes control and intelligent applications can be defined on top of this architecture. In the literature, diverse software-based applications exist, focusing on finding either the shortest paths, balancing the traffic, and others. However, they do not consider the potentially different level of security of links in the network. In this work, we propose an approach for Flow Admission and Routing under Minimal Security Constraints (FARSec) in Software Defined Networks, where network flows must use links which are at least as secure as their required security level. We prove that FARSec can find feasible paths respecting the minimum level of security for each flow. If the latter is not possible FARSec rejects the flow in order not to compromise its security. We show that the computational complexity of the proposed approach is polynomial. Experimental results with semi-random generated graphs confirm the efficiency and correctness of the proposed approach. Finally, we implement the proposed solution using OpenFlow and ONOS – an SDN open-source controller. We validate its functionality using an emulated network with various security levels.