Feature selection (FS) has received significant attention since the use of a well-selected subset of features may achieve better classification performance than that of full features in many real-world applications. It can be considered as a multiobjective optimization consisting of two objectives: 1) minimizing the number of selected features and 2) maximizing classification performance. Ant colony optimization (ACO) has shown its effectiveness in FS due to its problem-guided search operator and flexible graph representation. However, there lacks an effective ACO-based approach for multiobjective FS to handle the problematic characteristics originated from the feature interactions and highly discontinuous Pareto fronts. This article presents an Information-theory-based Nondominated Sorting ACO (called INSA) to solve the aforementioned difficulties. First, the probabilistic function in ACO is modified based on the information theory to identify the importance of features; second, a new ACO strategy is designed to construct solutions; and third, a novel pheromone updating strategy is devised to ensure the high diversity of tradeoff solutions. INSA's performance is compared with four machine-learning-based methods, four representative single-objective evolutionary algorithms, and six state-of-the-art multiobjective ones on 13 benchmark classification datasets, which consist of both low and high-dimensional samples. The empirical results verify that INSA is able to obtain solutions with better classification performance using features whose count is similar to or less than those obtained by its peers.