Intelligent reflecting surface (IRS) is a promising technology for beyond 5th Generation of the wireless communications. In fully passive IRS-assisted systems, channel estimation is challenging and should be carried out only at the base station or at the terminals since the elements of the IRS are incapable of processing signals. In this letter, we formulate a tensor-based semi-blind receiver that solves the joint channel and symbol estimation problem in an IRS-assisted multi-user multiple-input multiple-output system. The proposed approach relies on a generalized PARATUCK tensor model of the signals reflected by the IRS, based on a two-stage closed-form semi-blind receiver using Khatri-Rao and Kronecker factorizations. Simulation results demonstrate the superior performance of the proposed semi-blind receiver, in terms of the normalized mean squared error and symbol error rate, as well as a lower computational complexity, compared to recently proposed parallel factor analysis-based receivers.