Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) plays a significant role in breast cancer screening, cancer staging, and monitoring response to therapy. Recently, deep learning methods are being rapidly incorporated in image-based breast cancer diagnosis and prognosis. However, most of the current deep learning methods make clinical decisions based on 2-dimentional (2D) or 3D images and are not well suited for temporal image data. In this study, we develop a deep learning methodology that enables integration of clinically valuable temporal components of DCE-MRIs into deep learning-based lesion classification. Our work is performed on a database of 703 DCE-MRI cases for the task of distinguishing benign and malignant lesions, and uses the area under the ROC curve (AUC) as the performance metric in conducting that task. We train a recurrent neural network, specifically a long short-term memory network (LSTM), on sequences of image features extracted from the dynamic MRI sequences. These features are extracted with VGGNet, a convolutional neural network pre-trained on a large dataset of natural images ImageNet. The features are obtained from various levels of the network, to capture low-, mid-, and high-level information about the lesion. Compared to a classification method that takes as input only images at a single time-point (yielding an AUC = 0.81 (se = 0.04)), our LSTM method improves lesion classification with an AUC of 0.85 (se = 0.03).