UAVNs (unmanned aerial vehicle networks) may become vulnerable to threats and attacks due to their characteristic features such as high mobility, highly dynamic network topology, and open-air wireless environments. Since previous work has focused on classical and metaheuristic-based approaches, none of these approaches have a self-adaptive approach. In this article, we examine the challenges of cyber detection methods to secure UAVNs and review exiting security schemes proposed in the current literature. Furthermore, we propose an agent-based self-protective method (ASP-UAVN) for UAVNs that is based on the Human Immune System (HIS). In ASP-UAS, the safest route from the source UAV to the destination UAV is chosen according to a self-protective system. In this method, a multi-agent system using an Artificial Immune System (AIS) is employed to detect the attacking UAV and choose the safest route. In the proposed ASP-UAVN, the route request packet (RREQ) is initially transmitted from the source UAV to the destination UAV to detect the existing routes. Then, once the route reply packet (RREP) is received, a self-protective method using agents and the knowledge base is employed to choose the safest route and detect the attacking UAVs. The method is evaluated here via extensive simulations carried out in the NS-3 environment. The experimental results of four scenarios demonstrated that the ASP-UAS increases the Packet Delivery Rate (PDR) by more than 17.4, 20.8, and 25.91%, and detection rate by more than 17.2, 23.1, and 29.3%, and decreases the Packet Loss Rate (PLR) by more than 14.4, 16.8, and 20.21%, the false-positive and false-negative rate by more than 16.5, 25.3, and 31.21% those of SUAS-HIS, SFA and BRUIDS methods, respectively.