System identification, which infers the construction of a mathematical model of a dynamic system from time series records, is widely used to characterize system properties such as vibration frequencies, damping ratios, and mode shapes. This paper aims to quantify the variation in dynamic characteristics before and after the installation of block masonry infills. Although sequential construction is rarely allowed to be tested, we exploited this opportunity to test a special moment resisting reinforced concrete frame (SMRF) building right after the completion of the frame structure and following the installation of block masonry infills. Using the parametric state space system identification technique, the first three vibration frequencies of the bare frame system are determined as 3.20 Hz, 8.57 Hz, and 15.83 Hz, respectively along the long wall direction of the building and the same along the short wall direction are estimated respectively 2.83 Hz, 8.65 Hz, and 18.86 Hz. The damping ratio of the bare frame structure is found to be 1.66%. After the installation of block masonry, the first three mode vibration frequencies along the long wall direction are 4.77 Hz, 14.18 Hz, and 18.23 Hz, respectively. Meanwhile, the first three vibration frequencies along the short wall direction are found to be 3.55 Hz, 10.07 Hz, and 16.17 Hz, respectively. The damping ratio is estimated as 2.19%. We conclude that the installation of block masonry in RC frames considerably enhances stiffness and damping characteristics.