Fetal magnetic resonance imaging (MRI) is challenged by uncontrollable, large, and irregular fetal movements. It is, therefore, performed through visual monitoring of fetal motion and repeated acquisitions to ensure diagnostic-quality images are acquired. Nevertheless, visual monitoring of fetal motion based on displayed slices, and navigation at the level of stacks-of-slices is inefficient. The current process is highly operator-dependent, increases scanner usage and cost, and significantly increases the length of fetal MRI scans which makes them hard to tolerate for pregnant women. To help build automatic MRI motion tracking and navigation systems to overcome the limitations of the current process and improve fetal imaging, we have developed a new realtime image-based motion tracking method based on deep learning that learns to predict fetal motion directly from acquired images. Our method is based on a recurrent neural network, composed of spatial and temporal encoder-decoders, that infers motion parameters from anatomical features extracted from sequences of acquired slices. We compared our trained network on heldout test sets (including data with different characteristics, e.g. different fetuses scanned at different ages, and motion trajectories recorded from volunteer subjects) with networks designed for estimation as well as methods adopted to make predictions. The results show that our method outperformed alternative techniques, and achieved real-time performance with average errors of 3.5 and 8 degrees for the estimation and prediction tasks, respectively. Our real-time deep predictive motion tracking technique can be used to assess fetal movements, to guide slice acquisitions, and to build navigation systems for fetal MRI.