In this work, we address the problem of approximating minimum-size abductive explanations for decision trees using supermodular optimization. Finding a minimum-size abductive explanation is a time-intensive task, even for restricted classifiers like decision trees. This problem, being NP-hard for decision trees, makes exact approaches particularly time-consuming, especially for complex instances and high-dimensional data. To overcome these challenges, approximate or heuristic methods are often preferred, allowing for reduced computational load and faster results, albeit sometimes at the cost of optimality. Here, we propose a greedy algorithm to efficiently approximate minimum-size abductive explanations. Our experiments show that for difficult-to-explain instances, this algorithm provides an effective alternative to exact methods based on SAT encodings.