A distributed MIMO radar system consists of multiple transmitters, receivers, and a fusion center where the final target detection decision is made. It has previously been shown that a distributed MIMO radar offers improved performance compared with a conventional radar system due to the increased system diversity and degrees of freedom. However, as a complicated distributed system, it is vulnerable to cybersecurity attacks against its three key components: the transmitters, the receivers, and the communication links that connect them and the fusion center. In this paper, we investigate the impact of cybersecurity attacks on detection performance of a distributed MIMO radar. We show that the target detection performance degrades very significantly if the MIMO radar is not aware of the attacks. To mitigate the attacks, we develop robust detection schemes which can greatly improve detection performance when the radar is under attack.