Despite once being nearly eradicated, Measles cases in Europe have surged to a 20-year high with more than 60,000 cases in 2018, due to a dramatic decrease in vaccination rates. The decrease in Measles, Mumps, and Rubella (MMR) vaccination rates can be attributed to an increase in 'vaccine hesitancy', or the delay in acceptance or refusal of vaccines despite their availability. Vaccine hesitancy is a relatively new global problem for which effective interventions are not yet established. In this paper, a novel machine learning approach to identify children at risk of not being vaccinated against MMR is proposed, with the objective of facilitating proactive action by healthcare workers and policymakers. A use case of the approach is the provision of individualized informative guidance to families that may otherwise become or are already vaccine hesitant. Using a LASSO logistic regression model trained on 44,000 child Electronic Health Records (EHRs), vaccine hesitant families can be identified with a higher precision (0.72) than predicting vaccine uptake based on a child's infant vaccination record alone (0.63). The model uses a low number of attributes of the child and his or her family and community to produce a prediction, making it readily interpretable by healthcare professionals. The implementation of the machine learning model into an open source dashboard for use by healthcare providers and policymakers as an Early Warning and Monitoring System (EWS) against vaccine hesitancy is proposed. The EWS would facilitate a wide variety of proactive, anticipatory and therefore potentially more effective public health interventions, compared to reactive interventions taken after vaccine rejections.