We introduce the notion of non-Abelian tensors, and use them to build a general non-Abelian matrix product state (NA-MPS) ansatz. We construct a non-Abelian time evolving block decimation (NA-TEBD) scheme that uses an arbitrary number of Abelian and non-Abelian symmetries. Our approach increases the speed and memory storage efficiency of matrix product state based computations by several orders of magnitudes, and makes large bond dimensions accessible even on simple desktop architectures. We demonstrate our approach by studying post-quench dynamics in the repulsive SU(3) Hubbard model. We determine time evolution of various local operators and correlation functions and find that interactions turn algebraic charge relaxation into exponential, and  suppress coherent quantum oscillations rapidly.