The durability of concrete incorporating crumb rubber (CR) is adversely affected due to the incompatibility of the CR particles with other ingredients of conventional concrete. Consequently, efforts have been made to improve the durability of concrete by treating the CR. In the present work, the effect of treating CR with NaOH, KMnO4, and cement on the durability of concrete was evaluated. Concrete specimens were prepared with 2, 8, 16, 24, and 40% CR (by weight), partially replacing the sand used as fine aggregate. The durability of crumb rubber concrete (CRC) was evaluated by measuring its water absorption, acid resistance, electrical resistivity, and chloride permeability. The water absorption of CRC decreased due to the use of treated CR. This trend was particularly noted in concrete with high quantities of CR. The acid resistance of concrete with up to 8% NaOH-treated CRC was better than that of untreated-CRC. Although the weight loss was lowest in the KMnO4-treated CRC, the strength loss in this type of concrete was more than that of NaOH- and cement-treated CRC. The cement-treated CRC exhibited the best performance against acid attack even with 40% CR replacing the fine aggregate. A remarkable increase in the electrical resistivity and chloride permeability of CRC was noted due to the crucial changes in the pore structure of concrete containing treated-CR. The improvement in the durability of CRC encourages the use of CR so as to help conserve sand as a scarce commodity in many parts of the world. Moreover, the use of CR in concrete contributes to the circular economy of the world due to the utilization of a waste material, namely scrapped automobile tires.