Given a massive collection of sequences, it is infeasible to perform pairwise alignment for basic tasks like sequence clustering and search. To address this problem, we demonstrate that the MinHash technique, first applied to clustering web pages, can be applied to biological sequences with similar effect, and extend this idea to include biologically relevant distance and significance measures. Our new tool, Mash, uses MinHash locality-sensitive hashing to reduce large sequences to a representative sketch and rapidly estimate pairwise distances between genomes or metagenomes. Using Mash, we explored several use cases, including a 5,000-fold size reduction and clustering of all ~55,000 NCBI RefSeq genomes in 46 CPU hours. The resulting 93 MB sketch database includes all RefSeq genomes, effectively delineates known species boundaries, reconstructs approximate phylogenies, and can be searched in seconds using assembled genomes or raw sequencing runs from Illumina, Pacific Biosciences, and Oxford Nanopore. For metagenomics, Mash scales to thousands of samples and can replicate Human Microbiome Project and Global Ocean Survey results in a fraction of the time. Other potential applications include any problem where an approximate, global sequence distance is acceptable, e.g. to triage and cluster sequence data, assign species labels to unknown genomes, quickly identify mis-tracked samples, and search massive genomic databases. In addition, the Mash distance metric is based on simple set intersections, which are compatible with homomorphic encryption schemes. To facilitate integration with other software, Mash is implemented as a lightweight C++ toolkit and freely released under a BSD license at https://github.com/marbl/mash.