We propose Nazr-CNN1, a deep learning pipeline for object detection and fine-grained classification in images acquired from Unmanned Aerial Vehicles (UAVs) for damage assessment and monitoring. Nazr-CNN consists of two components. The function of the first component is to localize objects (e.g. houses or infrastructure) in an image by carrying out a pixel-level classification. In the second component, a hidden layer of a Convolutional Neural Network (CNN) is used to encode Fisher Vectors (FV) of the segments generated from the first component in order to help discriminate between different levels of damage. To showcase our approach we use data from UAVs that were deployed to assess the level of damage in the aftermath of a devastating cyclone that hit the island of Vanuatu in 2015. The collected images were labeled by a crowdsourcing effort and the labeling categories consisted of fine-grained levels of damage to built structures. Since our data set is relatively small, a pre-trained network for pixel-level classification and FV encoding was used. Nazr-CNN attains promising results both for object detection and damage assessment suggesting that the integrated pipeline is robust in the face of small data sets and labeling errors by annotators. While the focus of Nazr-CNN is on assessment of UAV images in a post-disaster scenario, our solution is general and can be applied in many diverse settings. We show one such case of transfer learning to assess the level of damage in aerial images collected after a typhoon in Philippines.