Monotonic classification is a kind of special task in machine learning and pattern recognition. Monotonicity constraints between features and decision should be taken into account in these tasks. However, most existing techniques are not able to discover and represent the ordinal structures in monotonic datasets. Thus, they are inapplicable to monotonic classification. Feature selection has been proven effective in improving classification performance and avoiding overfitting. To the best of our knowledge, no technique has been specially designed to select features in monotonic classification until now. In this paper, we introduce a function, which is called rank mutual information, to evaluate monotonic consistency between features and decision in monotonic tasks. This function combines the advantages of dominance rough sets in reflecting ordinal structures and mutual information in terms of robustness. Then, rank mutual information is integrated with the search strategy of min-redundancy and max-relevance to compute optimal subsets of features. A collection of numerical experiments are given to show the effectiveness of the proposed technique.