This paper is concerned with the detection of malicious attacks during the operation of switched systems. A novel game-theoretic switching detection scheme is proposed where the switching between subsystems is constructed aiming to reveal the existence of malicious attacks. The Kullback-Leibler (K-L) divergence between the legitimate and potentially falsified innovations is utilized as the stealthiness metric. Thereupon, a Stackelberg game is established to characterize the competition for stealthiness without any a priori restriction on the antagonistic attacker. Furthermore, the Stackelberg equilibrium switching strategy of the detector is implemented to orchestrate the activation among subsystems during the detection procedure, and the K-L divergence corresponding to the Stackelberg equilibrium is adopted as the detection threshold. Finally, as an example, a continuous stirred tank reactor is employed to demonstrate the effectiveness and applicability of the proposed results.