Nearest neighbor machine translation augments the Autoregressive Translation~(AT) with $k$-nearest-neighbor retrieval, by comparing the similarity between the token-level context representations of the target tokens in the query and the datastore. However, the token-level representation may introduce noise when translating ambiguous words, or fail to provide accurate retrieval results when the representation generated by the model contains indistinguishable context information, e.g., Non-Autoregressive Translation~(NAT) models. In this paper, we propose a novel $n$-gram nearest neighbor retrieval method that is model agnostic and applicable to both AT and NAT models. Specifically, we concatenate the adjacent $n$-gram hidden representations as the key, while the tuple of corresponding target tokens is the value. In inference, we propose tailored decoding algorithms for AT and NAT models respectively. We demonstrate that the proposed method consistently outperforms the token-level method on both AT and NAT models as well on general as on domain adaptation translation tasks. On domain adaptation, the proposed method brings $1.03$ and $2.76$ improvements regarding the average BLEU score on AT and NAT models respectively.