Many fluid dynamics systems exhibit extreme events, which are sudden and violent changes of the flow state. The time-accurate prediction of such events remains a major challenge because of the chaotic nature of turbulent flows, in which infinitesimal perturbations in the initial conditions will exponentially amplify. Recent advances in machine learning techniques have shown promises in learning and predicting the dynamics of such chaotic systems but their applicability to 3D turbulent flows remain unknown. In this work, we tackle this problem by proposing a 3D Convolutional AutoEncoded Echo State Network (CAE-ESN). First, with the CAE, we reduce the high-dimensional turbulent dynamics into a lower-dimensional latent space by using a nonlinear transformation based on convolutional neural networks. Second, with the ESN, we compute the temporal dynamics in the low-dimensional latent space by using the echo state network, which is a form of recurrent neural network. The test case is a three-dimensional turbulent flow, called the the minimal flow unit (MFU) in which quasi-relaminarization events with their bursts in kinetic energy and dissipation rate are the extreme events. We show that the CAE-ESN is able to accurately reproduce the velocity statistics of the MFU and time-accurately forecast the occurrence of the quasi-relaminarization events and their statistics.