Millimeter wave (mmWave) communication is a key component of 5G and beyond. Harvesting the gains of the large bandwidth and low latency at mmWave systems, however, is challenged by the sensitivity of mmWave signals to blockages; a sudden blockage in the line of sight (LOS) link leads to abrupt disconnection, which affects the reliability of the network. In addition, searching for an alternative base station to re-establish the link could result in needless latency overhead. In this paper, we address these challenges collectively by utilizing machine learning to anticipate dynamic blockages proactively. The proposed approach sees a machine learning algorithm learning to predict future blockages by observing what we refer to as the pre-blockage signature. To evaluate our proposed approach, we build a mmWave communication setup with a moving blockage and collect a dataset of received power sequences. Simulation results on a real dataset show that blockage occurrence could be predicted with more than 85% accuracy and the exact time instance of blockage occurrence can be obtained with low error. This highlights the potential of the proposed solution for dynamic blockage prediction and proactive hand-off, which enhances the reliability and latency of future wireless networks.