The application of machine translation in the field of poetry has always presented significant challenges. Conventional machine translation techniques are inadequate for capturing and translating the unique style of poetry. The absence of a parallel poetry corpus and the distinctive structure of poetry further restrict the effectiveness of traditional methods. This paper introduces a zero-shot method that is capable of translating poetry style without the need for a large-scale training corpus. Specifically, we treat poetry translation as a standard machine translation problem and subsequently inject the poetry style upon completion of the translation process. Our injection model only requires back-translation and easily obtainable monolingual data, making it a low-cost solution. We conducted experiments on three translation directions and presented automatic and human evaluations, demonstrating that our proposed method outperforms existing online systems and other competitive baselines. These results validate the feasibility and potential of our proposed approach and provide new prospects for poetry translation.