We present a novel methodology for the automated detection of breast lesions from dynamic contrast-enhanced magnetic resonance volumes (DCE-MRI). Our method, based on deep reinforcement learning, significantly reduces the inference time for lesion detection compared to an exhaustive search, while retaining state-of-art accuracy. This speed-up is achieved via an attention mechanism that progressively focuses the search for a lesion (or lesions) on the appropriate region(s) of the input volume. The attention mechanism is implemented by training an artificial agent to learn a search policy, which is then exploited during inference. Specifically, we extend the deep Q-network approach, previously demonstrated on simpler problems such as anatomical landmark detection, in order to detect lesions that have a significant variation in shape, appearance, location and size. We demonstrate our results on a dataset containing 117 DCE-MRI volumes, validating run-time and accuracy of lesion detection.