Concept drift detection is a crucial task in data stream evolving environments. Most of the state of the art approaches designed to tackle this problem monitor the loss of predictive models. Accordingly, an alarm is launched when the loss increases significantly, which triggers some adaptation mechanism (e.g. retrain the model). However, this modus operandi falls short in many real-world scenarios, where the true labels are not readily available to compute the loss. These often take up to several weeks to be available. In this context, there is increasing attention to approaches that perform concept drift detection in an unsupervised manner, i.e., without access to the true labels. We propose a novel approach to unsupervised concept drift detection, which is based on a student-teacher learning paradigm. Essentially, we create an auxiliary model (student) to mimic the behaviour of the main model (teacher). At run-time, our approach is to use the teacher for predicting new instances and monitoring the mimicking loss of the student for concept drift detection. In a set of controlled experiments, we discovered that the proposed approach detects concept drift effectively. Relative to the gold standard, in which the labels are immediately available after prediction, our approach is more conservative: it signals less false alarms, but it requires more time to detect changes. We also show the competitiveness of our approach relative to other unsupervised methods.