Histopathology images are crucial to the study of complex diseases such as cancer. The histologic characteristics of nuclei play a key role in disease diagnosis, prognosis and analysis. In this work, we propose a sparse Convolutional Autoencoder (CAE) for fully unsupervised, simultaneous nucleus detection and feature extraction in histopathology tissue images. Our CAE detects and encodes nuclei in image patches in tissue images into sparse feature maps that encode both the location and appearance of nuclei. Our CAE is the first unsupervised detection network for computer vision applications. The pretrained nucleus detection and feature extraction modules in our CAE can be fine-tuned for supervised learning in an end-to-end fashion. We evaluate our method on four datasets and reduce the errors of state-of-the-art methods up to 42%. We are able to achieve comparable performance with only 5% of the fully-supervised annotation cost.