Distributed control of modular multilevel converter (MMC) submodules (SMs) offers several potential benefits such as flexibility, scalability and modularity. In this approach, lowlevel control tasks, such as capacitor voltage balancing, can be distributed amongst controllers placed in the SMs. This decreases the computational burden for the central control system that performs high-level control tasks; also, a single point of failure is avoided. Distributed control architecture requires a cyberphysical network (CFN) through which local controllers share all the information necessary to perform their respective control loops. To date, none of the reported works in this field have paid attention to potential imperfections in the CFN. Indeed, previous works are based on the assumption that the network always provides correct information to the local controllers. However, erroneous measurements in the CFN may degrade the distributed control scheme operation, leading to suboptimal or even unstable operation. These events can occur in the presence of cyberattacks, for example, which can be created through illegitimate data intrusion into the distributed control architectures. This paper is the first to investigate the impacts of cyber-attacks on distributed control schemes used in MMCs. The effects of a specific cyber-attack, named false data injection attack (FDIA), on a consensus-based distributed control strategy are studied in this work. Additionally, a method for detecting FDIAs is proposed, along with a countermeasure strategy, to ensure the safe operation of the MMC whilst the attack is cleared. The proposals reported in this paper are validated using simulation and experimental results.