A promising strategy for next-generation wireless communication systems in pursuit of ultra-high information speed and extended coverage involves the synergistic integration of intelligent reflecting surfaces (IRS) with millimeter-wave multiple-input multiple-output (mmWave MIMO) systems. However, realizing the full potential of IRS-assisted mmWave MIMO systems necessitates precise channel state information (CSI). Existing CSI estimation methods for IRS-assisted mmWave hybrid (analog+digital) MIMO systems, such as orthogonal matching pursuit (OMP) and sparse Bayesian learning (SBL), require substantial number of pilots and exhibit high computational complexity due to their offline nature and requires matrix inversions. Consequently, these characteristics offer significant estimation delays and reduced spectral efficiency. To tackle these challenges, we propose an online variable step size zero attracting least mean square-based channel estimator to overcome the limitations of existing estimators. Moreover, we compare the accuracy of the proposed method with existing OMP, SBL, and oracle least squares (LSs) method, which is used for benchmarking purpose. Simulation results are presented to validate effectiveness of the suggested estimator in terms of accuracy, complexity, and pilot overhead requirements.