Recent investigations on the concept of modular metastructures have demonstrated remarkable adaptivity of properties as a synergistic product of assembling together metastable modules, modules that exhibit coexisting states for the same topology. It has been found that such modularity provides an accessible pathway for unprecedented massive property adaptation. Despite the extensive report on the static or quasistatic characteristics of modular metastructures, much remains to be explored regarding their dynamic characteristics. This research initiates the study on transient response of a modular metastructure under impulsive excitation. Numerical studies characterize the adaptability of energy exchange and localization characteristics afforded by metastable states. It is found that responses of internal bistable masses of the metastable modules play an important role in determining energy distribution of the overall system. It is discovered that low internal bistable mass and high impulsive energy level are beneficial for energy to be localized and dissipated internally. Additionally, mechanism behind effective energy absorption is disclosed. Overall, this investigation provides opportunities to tailor dynamical responses using modular metastructures and opens potential avenues for designing transient vibration absorbers.