Non-coding RNAs (ncRNAs) offer a wealth of therapeutic targets for a range of diseases. However, secondary structures and high similarity within sequence families make specific knockdown challenging. Here, we engineer a series of artificial oligonucleotide enzymes (XNAzymes) composed of 2’-deoxy-2’-fluoro-β-D-arabino nucleic acid (FANA) that specifically or preferentially cleave individual ncRNA family members under quasi-physiological conditions, including members of the classic microRNA cluster miR-17~92 (oncomiR-1) and the Y RNA hY5. We demonstrate self-assembly of three anti-miR XNAzymes into a biostable catalytic XNA nanostructure, which targets the cancer-associated microRNAs miR-17, miR-20a and miR-21. Our results provide a starting point for the development of XNAzymes as a platform technology for precision knockdown of specific non-coding RNAs, with the potential to reduce off-target effects compared with other nucleic acid technologies.