This study investigates the axial impact resistance and energy absorption of rubberized concrete with/without fiber-reinforced polymer confinement. The impact tests were carried out using an instrumented drop-weight testing apparatus. The experimental results have shown that rubberized concrete significantly reduced the maximum impact force of up to 50% and extended the impact duration. These characteristics make rubberized concrete a promising material for protective structures and particularly for future sustainable construction of rigid roadside barriers. Glass fiber–reinforced polymer confinement is a very effective method to improve the impact resistance for both conventional concrete and particularly for rubberized concrete. It was found that the rubberized concrete reduced the maximum impact force so that it transferred a lower force to a protected structure as well as a lower rebound force, which is desirable for protection of passengers in an incident of vehicle collision. Interestingly, the rubberized concrete showed a lower energy absorption capacity as compared to conventional concrete, where the exact reason for this is unknown to the authors. Therefore, further research is sought to provide more understanding of the response of rubberized concrete under impact and improve its energy absorption. This study explored experimentally the use of rubberized concrete as a promising sustainable construction material for applications to construction of columns in buildings located in seismic active zones or subjected to terrorist attack, security bollards and rigid road side barriers.