Prior works have shown the promising results of commonsense knowledge-aware models in improving informativeness while reducing the hallucination issue. Nonetheless, prior works often can only use monolingual knowledge whose language is consistent with the dialogue context. Except for a few high-resource languages, such as English and Chinese, most languages suffer from insufficient knowledge issues, especially minority languages. To this end, this work proposes a new task, Multi-Lingual Commonsense Knowledge-Aware Response Generation (MCKRG), which tries to use commonsense knowledge in other languages to enhance the current dialogue generation. Then, we construct a MCKRG dataset MCK-Dialog of seven languages with multiple alignment methods. Finally, we verify the effectiveness of using multi-lingual commonsense knowledge with a proposed MCK-T5 model. Extensive experimental results demonstrate the great potential of using multi-lingual commonsense knowledge in high-resource and low-resource languages. To the best of our knowledge, this work is the first to explore Multi-Lingual Commonsense Knowledge-Aware Response Generation.