Diffuse optical tomography (DOT) is an important functional imaging modality in clinical diagnosis and treatment. As the number of wavelengths in the acquired DOT data grows, it becomes very challenging to reconstruct diffusion and absorption coefficients of tissue, i.e., a DOT image. In this paper, we consider the hyperspectral DOT (hyDOT) inverse problem as a multiple-measurement vector (MMV) problem by exploiting the joint sparsity of the images to be reconstructed. Then we propose a fast stochastic greedy algorithm based on the MMV stochastic gradient matching pursuit (MStoGradMP) and the mini-batching technique. Numerical results show that the proposed algorithm can achieve higher reconstruction accuracy with significantly reduced running time than the related gradient descent method with sparsity regularization.