This paper addresses the cyber-threat detection and mitigation in a DC microgrid distributed control system. Due to the deployment of communication and control technologies, a DC microgrid resembles a cyber-physical system that is highly exposed to cyber-threats. A cyber-threat detection technique is proposed that relies on a Kullback-Liebler divergence-based criterion. This criterion detects the misbehavior of a compromised Distributed Energy Resource (DER) control unit and, consequently, calculates an interior-belief factor and communicates it with its neighboring DERs to inform them of the reliability of its outgoing information. Moreover, DERs calculate an exterior-belief value related to the trustworthiness of the received information from neighbors. The cyber-threat mitigation technique at each DER utilizes the neighbors' interior-belief and its own calculated exterior-belief value for neighboring DERs to slow down and eventually mitigate attacks. The proposed approach requires a communication network with mild graph connectivity. A typical medium-voltage DC microgrid system is simulated to verify the validity of proposed distributed cyber-secure control scheme. It is shown that using the proposed cyber-secure approach, the voltage of a critical bus of microgrid is well regulated and DERs can successfully distinguish cyber-attacks from legitimate events.