Measles is a highly contagious disease, one of the largest vaccine-preventable illnesses and leading causes of death in developing countries, claiming more than 140,000 lives each year. Measles was declared eliminated in the United States in the year 2000 due to decades of successful vaccination but it resurged in 2019 with 1,282 confirmed cases. Due to rapid spread of this disease among people in contact, rapid and automated diagnostic systems are required for early prevention. In this work, we employed transfer learning to build deep convolutional neural networks (CNNs) to distinguish measles rash from other skin conditions. Experiments with ResNet-50 model, trained on our diverse and curated skin rash image dataset, produce classification accuracy of 95.2%, sensitivity of 81.7%, and specificity of 97.1%, respectively. This indicates that our technique is effective in facilitating an accurate detection of measles to help contain outbreaks. The performance of a small CNN model MobileNet-V2 on our image data set is also discussed. Our work will facilitate healthcare professionals to effectively diagnose measles and accelerate the development of automated diagnostic tools to prevent the measles spread at various public venues.