Orthogonal time frequency space (OTFS) modulation, collaborated with millimeter-wave (mmWave) massive multiple-input-multiple-output (MIMO), is a promising technology for next generation wireless communications in high mobility scenarios. However, one of the main challenges for mmWave massive MIMO-OTFS systems is the enormous computational complexity of channel estimation incurred by the huge OTFS symbol size and the large number of antennas. To address this issue, in this paper, a tensor-based orthogonal matching pursuit (OMP) channel estimation algorithm is proposed by exploiting the channel sparsity in the delayDoppler-angle domain. In particular, we firstly propose a novel pilot design for the OTFS symbol structure in the frequency-time domain. Then, based on the proposed pilot structure, we formulate the channel estimation as a sparse signal recovery problem, and the tensor decomposition and parallel support detection are introduced into the tensor-based OMP algorithm to reduce the signal processing dimension significantly. Numerical simulations are performed to verify the superiority and the robustness of the proposed tensor-based OMP algorithm.