Detection of cell nuclei in microscopic images is a challenging research topic, because of limitations in cellular image quality and diversity of nuclear morphology, i.e. varying nuclei shapes, sizes, and overlaps between multiple cell nuclei. This has been a topic of enduring interest with promising recent success shown by deep learning methods. These methods train for example convolutional neural networks (CNNs) with a training set of input images and known, labeled nuclei locations. Many of these methods are supplemented by spatial or morphological processing. We develop a new approach that we call Shape Priors with Convolutional Neural Networks (SP-CNN) to perform significantly enhanced nuclei detection. A set of canonical shapes is prepared with the help of a domain expert. Subsequently, we present a new network structure that can incorporate 'expected behavior' of nucleus shapes via two components: learnable layers that perform the nucleus detection and a fixed processing part that guides the learning with prior information. Analytically, we formulate a new regularization term that is targeted at penalizing false positives while simultaneously encouraging detection inside cell nucleus boundary. Experimental results on a challenging dataset reveal that SP-CNN is competitive with or outperforms several state-of-the-art methods.