Surgical instrument segmentation in robot-assisted surgery (RAS) - especially that using learning-based models - relies on the assumption that training and testing videos are sampled from the same domain. However, it is impractical and expensive to collect and annotate sufficient data from every new domain. To greatly increase the label efficiency, we explore a new problem, i.e., adaptive instrument segmentation, which is to effectively adapt one source model to new robotic surgical videos from multiple target domains, only given the annotated instruments in the first frame. We propose MDAL, a meta-learning based dynamic online adaptive learning scheme with a two-stage framework to fast adapt the model parameters on the first frame and partial subsequent frames while predicting the results. MDAL learns the general knowledge of instruments and the fast adaptation ability through the video-specific meta-learning paradigm. The added gradient gate excludes the noisy supervision from pseudo masks for dynamic online adaptation on target videos. We demonstrate empirically that MDAL outperforms other state-of-the-art methods on two datasets (including a real-world RAS dataset). The promising performance on ex-vivo scenes also benefits the downstream tasks such as robot-assisted suturing and camera control.