Sequence labeling aims to predict a fine-grained sequence of labels for the text. However, such formulation hinders the effectiveness of supervised methods due to the lack of token-level annotated data. This is exacerbated when we meet a diverse range of languages. In this work, we explore multilingual sequence labeling with minimal supervision using a single unified model for multiple languages. Specifically, we propose a Meta Teacher-Student (MetaTS) Network, a novel meta learning method to alleviate data scarcity by leveraging large multilingual unlabeled data. Prior teacher-student frameworks of self-training rely on rigid teaching strategies, which may hardly produce high-quality pseudo-labels for consecutive and interdependent tokens. On the contrary, MetaTS allows the teacher to dynamically adapt its pseudo-annotation strategies by the student's feedback on the generated pseudo-labeled data of each language and thus mitigate error propagation from noisy pseudo-labels. Extensive experiments on both public and real-world multilingual sequence labeling datasets empirically demonstrate the effectiveness of MetaTS.