As more and more data are available as unbounded data streams rather than bounded data sets, machine learning methods that can update classification models over time are of particular interest. Hence, the question of combining the evolution of machine learning models with domain expertise arises. In particular, maintaining monotonicity constraints, encoding natural ordinal relationships between feature values and labels, is challenging in dynamic environments. Hence, in this work, we investigate the integration of monotonicity constraints with one of the main incremental learning methods, i.e., Hoeffding trees. We propose modifications to the Hoeffding trees, introducing mechanisms promoting monotonicity constraints while maintaining the ability to learn from streaming data. Through empirical evaluation of the novel Monotonicity-Constrained Hoeffding Trees (M-CHT) with real data, we demonstrate how these constraints affect prediction accuracy for binary classification tasks. Experiments performed with data from different domains show that not only can the proposed method consider monotonicity constraints, but also that the M-CHT method can yield improved classification accuracy compared to the standard Hoeffding tree method.