A new diagnostic method to identify the location and magnitude of external impact on a sandwich structure using granular crystal sensors was studied. The granular crystal sensors are composed of one-dimensional chains of spherical particles that are inserted in a thick core of the sandwich structure. Given an external impact, the embedded sensors generate compact-supported, highly nonlinear solitary waves resulting from the dispersive and nonlinear characteristics of granular crystals. In this study, the propagating mechanism of highly nonlinear solitary waves in relation to various impact conditions was investigated. Particularly, it was reported that the flight time and magnitude of solitary waves are highly sensitive to the location and amplitude of impact. By analyzing measured solitary waves, the striker’s impact location and drop height was successfully predicted nondestructively. It was found that the diagnostic results are in agreement with the numerical simulations obtained from a combined spectral element and discrete element model. The findings in this study imply that the granular crystal sensors can form a new type of impact monitoring system for a sandwich structure to achieve enhanced diagnostic accuracy and potentially to improve sensors’ survivability under harsh mechanical and thermal environments.