The recent advancements in unmanned aerial vehicles (UAVs) upsurges its usages in commercial and civilian applications such as surveillance, rescue, and crowdsensing. UAVs are vulnerable to being destroyed, lost, or stolen in case of security breaches of its network. The network management of UAVs is a crucial task due to its high mobility, which necessitates UAV network softwarization. Then, it becomes indispensable that allows the separation of control functions (i.e., control plane data) from hardware for smooth execution of complex operations. Further, UAV uses the Internet (an open channel) for communication in its complex system that raises a network security concern. The well-known softwarization techniques, i.e., software-defined networking (SDN) and network function virtualization (NFV) can be used to accomplish the secure network services on less expense. Conversely, these softwarization techniques may suffer from various threats like access control, user authentication, controller hijacking, and many more attack. The existing solutions are using a centralized system, which is having a single point of failure issue and vulnerable to security threats. Motivated from these facts, we present a comprehensive and systematic survey on the blockchain-based softwarization for a secure UAV network. Then, we propose a blockchain-enabled UAV softwarization architecture for secure communication and network management. It provides dynamic, flexible, and on-the-fly decision capabilities for communication services over the UAV network. Eventually, we analyzed the open research issues and challenges for future research directions in this emerging area.