Feature selection or dimensionality reduction can be considered as a multi-objective minimization problem with two objectives: minimizing the number of features and minimizing the error rate simultaneously. Despite being a multi-objective problem, most existing approaches treat feature selection as a single-objective optimization problem. Recently, Multi-objective Grey Wolf optimizer (MOGWO) was proposed to solve multi-objective optimization problem. However, MOGWO was originally designed for continuous optimization problems and hence, it cannot be utilized directly to solve multi-objective feature selection problems which are inherently discrete in nature. Therefore, in this research, a binary version of MOGWO based on sigmoid transfer function called BMOGW-S is developed to optimize feature selection problems. A wrapper based Artificial Neural Network (ANN) is used to assess the classification performance of a subset of selected features. To validate the performance of the proposed method, 15 standard benchmark datasets from the UCI repository are employed. The proposed BMOGWO-S was compared with MOGWO with a tanh transfer function and Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi-objective Particle Swarm Optimization (MOPSO). The results showed that the proposed BMOGWO-S can effectively determine a set of non-dominated solutions. The proposed method outperforms the existing multi-objective approaches in most cases in terms of features reduction as well as classification error rate while benefiting from a lower computational cost.