We study the problem of active learning for multilabel classification. We focus on the real-world scenario where the average number of positive (relevant) labels per data point is small leading to positive label sparsity. Carrying out mutual information based near-optimal active learning in this setting is a challenging task since the computational complexity involved is exponential in the total number of labels. We propose a novel inference algorithm for the sparse Bayesian multilabel model of [17]. The benefit of this alternate inference scheme is that it enables a natural approximation of the mutual information objective. We prove that the approximation leads to an identical solution to the exact optimization problem but at a fraction of the optimization cost. This allows us to carry out efficient, non-myopic, and near-optimal active learning for sparse multilabel classification. Extensive experiments reveal the effectiveness of the method.