Motor adaptation displays a structure-learning effect: adaptation to a new perturbation occurs more quickly when the subject has prior exposure to perturbations with related structure. Although this `learning-to-learn' effect is well documented, its underlying computational mechanisms are poorly understood. We present a new model of motor structure learning, approaching it from the point of view of deep reinforcement learning. Previous work outside of motor control has shown how recurrent neural networks can account for learning-to-learn effects. We leverage this insight to address motor learning, by importing it into the setting of model-based reinforcement learning. We apply the resulting processing architecture to empirical findings from a landmark study of structure learning in target-directed reaching (Braun et al., 2009), and discuss its implications for a wider range of learning-to-learn phenomena.