This paper proposes a tensor-based parametric channel estimation technique for IRS-assisted communication systems with time-varying channel parameters. We exploit the multidimensional structure of the received signal by developing a $3$rd-order PARAFAC tensor model that is solved by employing the iteratively ALS algorithm. Our simulation results show that the proposed approach provides enhanced performance in terms of NMSE of the concatenated channel compared to the competing solutions by capitalizing on the intrinsic tensor structure of the received signal without increasing the computational complexity of the channel estimation.