The ability to predict the future intended movement is crucial for collaborative robots to anticipate the human actions and for assistive technologies to alert if a particular movement is non-ergonomic and potentially dangerous for the human health. In this paper, we address the problem of predicting the future human whole-body movements given early observations. We propose to predict the continuation of the high-dimensional trajectories mapped into a reduced latent space, using autoencoders (AE). The prediction is based on a probabilistic description of the movement primitives (ProMPs) in the latent space, which notably reduces the computational time for the prediction to occur, and hence enables to use the method in real-time applications. We evaluate our method, named AE-ProMPs, for predicting future movements belonging to a dataset of 7 different actions performed by a human, recorded by a wearable motion tracking suit.