In this paper three historical masonry minarets in Istanbul, Turkey, are assessed for the dependency between the input harmonic motion and structural response parameters. Their heights are 40, 73 and 74 m, while the slenderness is 12, 6 and 12, respectively. The discrete element method is used in dynamic nonlinear analyses. Models were calibrated with measured natural frequencies. A series of sine-wave excitations is created for different frequency-amplitude pairs varying between 0.4 and 10 Hz, and between 0.1 and 1 m/s. From the results of dynamic simulations, a general trend was observed for masonry minarets. Especially, slenderness and wall thickness play an important role on their dynamic response and damage pattern. Dynamic behavior of these minarets cannot reliably be estimated by static non-linear analysis. Two engineering demand parameters (EDPs) are defined to characterize the displacement of the minaret top and the inter-ring shear displacements along the minaret body. Damage performance criteria for minarets are proposed based on four damage states and tentative limit values are given. We were able to identify the occurrence of those limit states as a function of frequency and amplitude of sinusoidal input motion.