In this paper, a distributed consensus-based formation control of networked nonholonomic mobile robots using neural networks (NN) in the presence of uncertain robot dynamics with event-based communication is presented. The robots communicate their location and velocity information with their neighbors, at event-based sampling instants, to drive themselves to a pre-defined desired formation by using distributed controllers. For relaxing the perfect velocity tracking assumption, control torque is designed to reduce the velocity tracking error by explicitly taking into account each robot dynamics and the formation dynamics of the network of robots via NN approximation. The approximated dynamics are employed to generate the control torque with event-sampled measurement updates and communication. For the distributed formation control scheme, Lyapunov stability theory is utilized to develop decentralized event-sampling condition and to demonstrate that the robots reach a consensus in their regulation errors. Finally, simulation results are presented to verify theoretical claims and to demonstrate the reduction in computations and communication cost.