We describe a multi-task learning approach to train a Neural Machine Translation (NMT) model with a Relevance-based Auxiliary Task (RAT) for search query translation. The translation process for Cross-lingual Information Retrieval (CLIR) task is usually treated as a black box and it is performed as an independent step. However, an NMT model trained on sentence-level parallel data is not aware of the vocabulary distribution of the retrieval corpus. We address this problem and propose a multi-task learning architecture that achieves 16% improvement over a strong baseline on Italian-English query-document dataset. We show using both quantitative and qualitative analysis that our model generates balanced and precise translations with the regularization effect it achieves from multi-task learning paradigm.