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This article studies the fault detection problem for a class of discrete‐time impulsive systems using mixed dissipativity theory. First, under the impulsive effects, a fault diagnosis observer is designed such that it is insensitive to disturbances, and sensitive to faults. Then, a mixed dissipativity concept is introduced to deal with impulsive effects, disturbances insensitivity condition and faults sensitive condition in one framework such that the impulsive error dynamic is dissipative with respect to the proposed mixed supply rate. Based on the proposed mixed supply rate, sufficient conditions are obtained to guarantee the dissipativity of the impulsive estimation error dynamic. Moreover, sufficient conditions are established for the existence of the desired fault observer. The corresponding solubility conditions for the designs of the desired observer are also obtained. Finally, simulation results are proposed to demonstrate the effectiveness of our proposed strategy.