Though nearest neighbor Machine Translation (kNN-MT) (CITATION) has proved to introduce significant performance boosts over standard neural MT systems, it is prohibitively slow since it uses the entire reference corpus as the datastore for the nearest neighbor search. This means each step for each beam in the beam search has to search over the entire reference corpus. kNN-MT is thus two-orders slower than vanilla MT models, making it hard to be applied to real-world applications, especially online services. In this work, we propose Fast kNN-MT to address this issue. Fast kNN-MT constructs a significantly smaller datastore for the nearest neighbor search: for each word in a source sentence, Fast kNN-MT first selects its nearest token-level neighbors, which is limited to tokens that are the same as the query token. Then at each decoding step, in contrast to using the entire corpus as the datastore, the search space is limited to target tokens corresponding to the previously selected reference source tokens. This strategy avoids search through the whole datastore for nearest neighbors and drastically improves decoding efficiency. Without loss of performance, Fast kNN-MT is two-orders faster than kNN-MT, and is only two times slower than the standard NMT model. Fast kNN-MT enables the practical use of kNN-MT systems in real-world MT applications. The code is available at https://github.com/ShannonAI/fast-knn-nmt.