In this paper, a nonlinear low-velocity impact analysis of a rectangular composite plate reinforced with Shape Memory Alloy (SMA) strips is conducted, and the effect of the impactor's energy on the impact response of the plate is investigated. In this research, in order to extract accurate results that can be utilized for the validation of future theoretical findings, the instantaneous changes and spatial non-uniformity of the austenite-to-martensite phase transformation (and vice versa) have been considered for the first time. Furthermore, instead of utilizing approximate plate theories, three-dimensional simulation has been employed to extract impact responses based on the theory of three-dimensional elasticity, the implicit result of which is the modification of the contact law. The analysis results demonstrate that the SMA, by forming a hysteresis loop during the impact, leads to a reduction in the energy absorbed by the composite plate; the result of this is an increase in the impact resistance of the composite plate and a reduction in the resulting damage. Moreover, the results indicate that by increasing the impactor's energy, the martensite fraction, contact force, and the deflection at the point of impact increase. The contact duration increases when the impact energy is increased by increasing the impactor's mass; however, it decreases when the impact energy is increased by increasing the impactor's velocity.