Nowadays, 3D objects are frequently stored and shared online, where they become vulnerable to attacks. Therefore, applying security measures such as encryption is crucial. Once the 3D object is encrypted and stored online, a third party who is not authorized to access the content of the 3D object may need to embed hidden data in the 3D object. In this paper, we propose a new MSB-based reversible data-hiding in the encrypted domain method for 3D objects, which uses a Hamiltonian path to establish a unique order for the vertices of a 3D object. For the reconstruction step, we select the smallest distance between vertices to accurately predict the MSB value of the mantissa for each coordinate. Our proposed method is format compliant, avoids any size expansion, and does not require auxiliary file, while guaranteeing the reversibility of the marked encrypted 3D object, even when tested on a large database of 3D objects.