A key challenge in studying organisms and diseases is to detect rare molecular programs and rare cell populations that drive development, differentiation and transformation. Molecular features, such as genes and proteins, defining rare cell populations are often unknown and are difficult to detect from unenriched single-cell data using conventional dimensionality reduction and clustering-based approaches. Here, we propose an unsupervised approach, SCMER (‘single-cell manifold-preserving feature selection’), which selects a compact set of molecular features with definitive meanings that preserve the manifold of the data. We apply SCMER in the context of hematopoiesis, lymphogenesis, tumorigenesis and drug resistance and response. We find that SCMER can identify non-redundant features that sensitively delineate both common cell lineages and rare cellular states. SCMER can be used for discovering molecular features in a high-dimensional dataset, designing targeted, cost-effective assays for clinical applications and facilitating multi-modality integration.