The use of automated insulin injection systems has become increasingly common for management of diabetes. However, these systems are vulnerable to cyberattacks, which can compromise the safety and effectiveness of the treatment. One type of cyberattack that has been identified in these systems is the replay attack, in which the hacker intercepts and replays legitimate data in order to manipulate the insulin delivery. In this paper, we propose a replay cyberattack detection system based on a feasibility condition that is developed and investigated. Towards this end, we add a virtual auxiliary system and detection filters to the automated control system. The key advantage of our proposed methodology is that the proposed scheme makes the system resilient to undetectable replay cyberattacks where the filters are capable of isolating replay cyberattacks from other types of adversary cyberattacks. The simulation results are provided to illustrate the effectiveness of the proposed approach.