Biological data, including gene expression data, are generally high-dimensional and require efficient, generalizable, and scalable machine-learning methods to discover complex nonlinear patterns. Recent advances in machine learning can be attributed to deep neural networks (DNNs), which perform various tasks in terms of computer vision and natural language processing. However, standard DNNs are inappropriate for high-dimensional datasets generated in biology because they consider numerous parameters, which in turn require numerous samples. In this paper, we propose a DNN-based, nonlinear feature selection method, called the feature selection network (FsNet), for high-dimensional and small sample data. Specifically, FsNet comprises a selection layer that selects features and a reconstruction layer that stabilizes the training. Because a large number of parameters in the selection and reconstruction layers can easily result in overfitting under a limited number of samples, we utilized two tiny networks to predict the large virtual weight matrices of the selection and reconstruction layers. Experimental results on several real-world high-dimensional biological datasets demonstrate the efficacy of the proposed method.