Operational Modal Analysis (OMA) method is frequently used in order to determine dynamical properties of historical masonry structures. In this study, damage pattern of historical Alaca minaret which is selected as application is investigated under different ground motions by updating finite element models (FEM) depending on operational modal analysis test. Initial Finite element model was prepared in ABAQUS V10 program and numerical dynamic characteristics of minaret were determined. In addition, experimental dynamic properties of minaret were provided by operational modal analysis. Initial numerical model of brick masonry structure was calibrated via OMA method. Then, linear and non-linear seismic analyses of calibrated FEM of historical minaret were performed by using different earthquakes acceleration records that occurred in Turkey. Concrete Damage Plasticity model was taken into account in non-linear seismic analyses. As a result of the analyses, it is concluded that the stresses obtained with linear analyses aren't as realistic as the non-linear analyses results and the earthquakes can cause some damages in the minaret.