We present in this paper a parallel algorithm that generates a low-rank approximation of a distributed tensor using QR decomposition with tournament pivoting (QRTP). The algorithm generates factor matrices for a Tucker decomposition by applying QRTP to the unfolding matrices of a tensor distributed block-wise (by sub-tensor) on a set of processors. For each unfolding mode the algorithm logically reorganizes (unfolds) the processors so that the associated unfolding matrix has a suitable logical distribution. We also establish error bounds between a tensor and the compressed version of the tensor generated by the algorithm.