<div>This paper introduces a novel shallow self-supervised tensor neural network for volumetric segmentation of brain MR images obviating training or supervision. The proposed network is a 3D version of the Quantum-Inspired Self Supervised Neural Network (QIS-Net) architecture and is referred to as 3D Quantum-inspired Self-supervised Tensor Neural Network (3D-QNet). The underlying architecture of 3D-QNet is composed of a trinity of volumetric layers viz. input, intermediate and output layers inter-connected using a 26-connected third-order neighborhood-based topology for voxel-wise processing of 3D MR image data suitable for semantic segmentation. Each of the volumetric layers contains quantum neurons designated by qubits or quantum bits. The incorporation</div><div>of tensor decomposition in quantum formalism leads to faster convergence of the network operations to preclude the inherent slow convergence problems faced by the self-supervised networks. The segmented volumes are obtained once the network converges. The suggested 3D-QNet is tailored and tested on the BRATS 2019 data set extensively in the experiments carried out. 3D-QNet has achieved promising dice similarity while compared with the intensively supervised convolutional network-based models 3D-UNet, Vox-ResNet, DRINet, and 3D-ESPNet, thus facilitating annotation free semantic segmentation using a self-supervised shallow network.</div>