Physical Internet (PI) is a global and interconnected logistics system that enables freight transportation and material handling akin to transfer of data packets in computer networks and digital Internet. Blockchain is an emerging and disruptive technology that has the potential to bring ground-breaking innovation and major improvements to PI based transportation and material handling systems. In this article, we describe the advantages of integrating blockchain technology with PI and present suitable architectures. We discuss the enabling concepts required to ensure the feasibility of blockchain based PI networks leading to efficiency and trust for the next generation logistic networks and material handling systems. Furthermore, we present two permissioned block-chain architectures using Hyperledger Fabric and Besu that provide decentralization, privacy, trust, immutability, and transparency in PI networks. Finally, we highlight several use case scenarios that demonstrate the practicality of the proposed blockchain architectures for the PI networks.