The Physical Internet (PI) offers an innovative approach to logistics networks, focussing on operational, digital, and physical interconnectivity through encapsulation, interfaces, and protocols. However, PI network can be complex to manage due to its dynamic structure and the need for routing protocols that adapt to continually evolving circumstances. This paper proposes a dynamic and reactive routing protocol for a PI sub-network, leveraging well-known Internet techniques, namely ‘Route Request’ and ‘Route Reply’. The objective is to enable dynamic, self-starting, multi-hop routing among nodes, ensuring continuous connectivity even amidst network disruptions. Moreover, the protocol incorporates reactive assignment algorithms to address disruptions, such as product shortages and resource unavailability. Additionally, the protocol is innovative in considering each container and resource's preferences and local knowledge of the system's known state. To include preferences in decision-making, we incorporate the Technique for Order Preference by Similarity to Ideal Solution and goal programming. Finally, we use multi-agent simulation and real order data from two major French retail chains to evaluate the protocol's performance. Results showed improved routing robustness and efficiency amidst disruptions compared to state-of-the-art methods. Various scenarios have been examined to yield promising insights for future research and practical applications in the realm of the PI.