Contemporary molecular biology deals with a wide and heterogeneous set of measurements to model and understand underlying biological processes including complex diseases. Machine learning provides a frequent approach to build such models. However, the models built solely from measured data often suffer from overfitting, as the sample size is typically much smaller than the number of measured features. In this paper, we propose a random forest-based classifier that minimizes this overfitting with the aid of prior knowledge in the form of a feature interaction network. We illustrate the proposed method in the task of disease classification based on measured mRNA and miRNA profiles complemented by the interaction network composed of the miRNA-mRNA target relations and mRNA-mRNA interactions corresponding to the interactions between their encoded proteins. We demonstrate that the proposed network-constrained forest employs prior knowledge to increase learning bias and consequently to improve classification accuracy, stability and comprehensibility of the resulting model. The experiments are carried out in the domain of myelodysplastic syndrome that we are concerned about in the long term. We validate our approach in the public domain of ovarian carcinoma, with the same data form. We believe that the idea of a network-constrained forest can straightforwardly be generalized towards arbitrary omics data with an available and non-trivial feature interaction network.