In this paper, the covert communication scenario over K-user-pair discrete memoryless interference channels with a warden is studied. We assume that the wardens channel output distribution induced by K "off input symbols, which are sent when no communication occurs, is not a convex combination of those induced by any other combination of input symbols (otherwise, the square-root law does not hold). We derive the exact covert capacity region and show that a simple point-topoint based scheme with treating interference as noise is optimal. In addition, we analyze the secret key length required for the reliable and covert communication with the desired rates, and present a channel condition where the secret key between each user pair is unnecessary.