Over the last decade, excessive devastations caused by extreme events, such as blast loading have raised significant concern on the performance of civil structural systems. Despite realizing the importance of inherent risk associated with this phenomenon, most of the studies neglected the effects of uncertainties associated with the system, wherein the design approaches have been entirely on deterministic scale. Hence, it is deemed important to identify the complexities in the system, and in this regard, a probabilistic framework is proposed which utilizes the effects of uncertainties in the system to compute the failure probabilities of a reinforced concrete (RC) structural member under extreme blast loading. The structural member adopted here is a three-dimensional (3-D) RC wall panel, which is modeled considering material and geometric nonlinearity, and the subsequent analysis is carried out under surface-burst and free airburst scenarios. High strain rate effect induced in the RC wall is modeled using available standard dynamic increase factors (DIFs) for concrete and steel. Uncertainty in the system is assumed in material capacity (strength), mechanical loads, and dynamic blast loads considering a certain mean and standard deviation. Responses are obtained in terms of deflection, stresses, and strains at center of the wall. Limit state of failure and the respective threshold limiting values are obtained from the United States Department of Defense manual, PDC-TR 06-08 (2008). Finally, first-order sensitivity analysis is conducted to show the extent of uncertainties in input parameters affecting the output response quantities. It is concluded that the uncertainty induced in the system has significant influence in the response of the wall panels under blast loading scenarios. Moreover, based on the sensitivity analysis performed, charge weight, standoff distance, and strength of concrete material are suggested to be crucial parameters for design of blast-resistant structures. To conclude, based on the currently considered scenario of intensity of blast, exposure type, and performance level required by the user, it is recommended to use wall panels of sizes more than 100 mm in civil structures, especially 125 mm to counter the effects of extreme blast loadings.