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Unsupervised machine translation, which utilizes unpaired monolingual corpora as training data, has achieved comparable performance against supervised machine translation. However, it still suffers from data-scarce domains. To address this issue, this paper presents a novel meta-learning algorithm for unsupervised neural machine translation (UNMT) that trains the model to adapt to another domain by utilizing only a small amount of training data. We assume that domain-general knowledge is a significant factor in handling data-scarce domains. Hence, we extend the meta-learning algorithm, which utilizes knowledge learned from high-resource domains, to boost the performance of low-resource UNMT. Our model surpasses a transfer learning-based approach by up to 2-4 BLEU scores. Extensive experimental results show that our proposed algorithm is pertinent for fast adaptation and consistently outperforms other baseline models.