In this study, a parametric study is conducted to determine the stochastic dynamic response of a historical masonry bridge under blast-induced ground motions. With this purpose, an existing historical masonry bridge located in Turkey, called Kurt Bridge is considered and analyzed under blast-induced multi-point random ground motion. This sample bridge model reflects almost all of the structural characteristics of similar type historical masonry arch bridges whereby the results of this study can be generalized to similar structural systems. Blast-induced ground motion which is random in nature is described by power spectrum of a white noise process and is applied to support points of three-dimensional finite element model of the considered bridge system. To underline the importance of the blast-induced multi-point ground motion, three support regions are defined for the application of the random ground motion. Different charge weights and distances from the charge center are considered while determining the power spectral density functions. Depending on the considered charge weights and charge center distances power spectral density functions and shaded image counters of one standard deviation of the responses of the masonry bridge are determined. The results of the analyses show that blast-induced multi-point ground motion causes smaller structural responses if compared with those of the responses obtained from the blast-induced uniform ground motion.