In recent years, hyperspectral imaging (HSI) has been shown as a promising imaging modality to assist pathologists in the diagnosis of histological samples. In this work, we present the use of HSI for discriminating between normal and tumor breast cancer cells. Our customized HSI system includes a hyperspectral (HS) push-broom camera, which is attached to a standard microscope, and home-made software system for the control of image acquisition. Our HS microscopic system works in the visible and near-infrared (VNIR) spectral range (400 - 1000 nm). Using this system, 112 HS images were captured from histologic samples of human patients using 20× magnification. Cell-level annotations were made by an expert pathologist in digitized slides and were then registered with the HS images. A deep learning neural network was developed for the HS image classification, which consists of nine 2D convolutional layers. Different experiments were designed to split the data into training, validation and testing sets. In all experiments, the training and the testing set correspond to independent patients. The results show an area under the curve (AUCs) of more than 0.89 for all the experiments. The combination of HSI and deep learning techniques can provide a useful tool to aid pathologists in the automatic detection of cancer cells on digitized pathologic images.