Finding non-linear relationships between biomolecules and a biological outcome is computationally expensive and statistically challenging. Existing methods have important drawbacks, including among others lack of parsimony, non-convexity and computational overhead. Here we propose block HSIC Lasso, a non-linear feature selector that does not present the previous drawbacks. We compare block HSIC Lasso to other state-of-the-art feature selection techniques in both synthetic and real data, including experiments over three common types of genomic data: gene-expression microarrays, single-cell RNA sequencing and genome-wide association studies. In all cases, we observe that features selected by block HSIC Lasso retain more information about the underlying biology than those selected by other techniques. As a proof of concept, we applied block HSIC Lasso to a single-cell RNA sequencing experiment on mouse hippocampus. We discovered that many genes linked in the past to brain development and function are involved in the biological differences between the types of neurons. Block HSIC Lasso is implemented in the Python 2/3 package pyHSICLasso, available on PyPI. Source code is available on GitHub (https://github.com/riken-aip/pyHSICLasso). Supplementary data are available at Bioinformatics online.