Traditional methods for solvability region analysis can only have inner approximations with inconclusive conservatism and handle limited types of power flow models. In this letter, we propose a deep active learning framework for solvability prediction in power systems. Compared with passive learning where the training is performed after all instances are labeled, active learning selects most informative instances to be labeled and therefore significantly reduces the size of the labeled dataset for training. In the active learning framework, the acquisition functions, which correspond to different sampling strategies, are defined in terms of the on-the-fly posterior probability from the classifier. First, the IEEE 39-bus system is employed to validate the proposed framework, where a two-dimensional case is illustrated to visualize the effectiveness of the sampling method followed by the high-dimensional numerical experiments. Then, the Northeast Power Coordinating Council (NPCC) 140-bus system is used to validate the performance on large-scale power systems.