Collaborative Inference (CI) optimizes the latency and energy consumption of deep learning inference through the inter-operation of edge and cloud devices. Albeit beneficial for other tasks, CI has never been applied to the sequence- to-sequence mapping problem at the heart of Neural Machine Translation (NMT). In this work, we address the specific issues of collaborative NMT, such as estimating the latency required to generate the (unknown) output sequence, and show how existing CI methods can be adapted to these applications. Our experiments show that CI can reduce the latency of NMT by up to 44% compared to a non-collaborative approach.