The comet assay is a technique used to assess the DNA damage in individual cells. The extent of the damage is indicated by the ratio between the amount of DNA in the tail of the comet and the amount in the head. This assessment is typically made by the operator manually analyzing the images. This process is inefficient and time consuming. Researchers in the past have used machine learning techniques to automate this process but it required manual feature extraction. In some cases, deep learning was applied but only for damage classification. We have successfully applied Convolutional Neural Networks(CNN) to achieve automated quantification of DNA damage from comet images. Typically deep learning techniques such as CNN require large amounts of labelled training data, which may not always be available. We demonstrate that by applying deep transfer learning, state of the art results can be obtained in the detection of DNA damage, even with a limited number of comet images.