Recent technological improvements have revolutionized the wireless sensor network-based industrial sector with the emergence of Internet of Things. Internet of Drones, a branch of Internet of Things, is used for the communication among drones. As drones are mobile in nature, they cause frequent topological changes. This changing topology causes scalability, stability, and route selection issues in Internet of Drones. To handle these issues, we propose a bio-inspired clustering scheme using dragonfly algorithm for cluster formation and management. In this article, we propose cluster head election based on the connectivity with the base station along with the fitness function which consists of residual energy and position of the drones. Furthermore, for route selection we propose an optimal path selection based on the residual energy and position of drone for efficient communication. The proposed scheme shows better results as compared to other bio-inspired clustering algorithms on the basis of evaluation benchmarks such as cluster building time, network energy consumption, cluster lifetime, and probability of successful delivery. The results indicate that the proposed scheme has improved 60% and 38% with respect to ant colony optimization and grey wolf optimization, respectively, in terms of average cluster building time while average energy consumption has improved 23% and 33% when compared to the ant colony optimization and grey wolf optimization, respectively.