The synergistic integration of the intelligent reflecting surface (IRS) and millimeter wave (mmWave) multiple-input multiple-output (MIMO) system is a potential solution for future wireless communication systems, aiming to achieve exceptionally high data rates with enhanced coverage. However, estimation of the cascaded channel state information is essential for beamforming in mmWave MIMO systems with IRS. Unlike conventional MIMO systems, channel estimation for IRS-aided mmWave MIMO systems is challenging due to the limited signal processing capability of the IRS. In this letter, we propose an online sparse exponential forgetting window least mean square-based channel estimator for IRS-assisted mmWave hybrid MIMO systems. Furthermore, we compare accuracy of the proposed estimator with the existing sparse estimators such as orthogonal matching pursuit, sparse Bayesian learning, and oracle least square for benchmarking. Additionally, we perform an analysis of the spectral efficiency and computational complexity of the proposed algorithms. Simulations corroborate superior performance of the proposed method in terms of accuracy, complexity, and robustness.