This paper explores machine learning to address a problem of Partially Observable Multi-sensor Sequential Change Detection (POMSCD), where only a subset of sensors can be observed to monitor a target system for change-point detection at each online learning round. In contrast to traditional Multisensor Sequential Change Detection tasks where all the sensors are observable, POMSCD is much more challenging because the learner not only needs to detect on-the-fly whether a change occurs based on partially observed multi-sensor data streams, but also needs to cleverly choose a subset of informative sensors to be observed in the next learning round, in order to maximize the overall sequential change detection performance. In this paper, we present the first online learning study to tackle POMSCD in a systemic and rigorous way. Our approach has twofold novelties: (i) we attempt to detect changepoints from partial observations effectively by exploiting potential correlations between sensors, and (ii) we formulate the sensor subset selection task as a Multi-Armed Bandit (MAB) problem and develop an effective adaptive sampling strategy using MAB algorithms. We offer theoretical analysis for the proposed online learning solution, and further validate its empirical performance via an extensive set of numerical studies together with a case study on real-world data sets.