We present a machine learning approach that uses a custom Convolutional Neural Network (CNN) for estimating the depth of water pools from multispectral drone imagery. Using drones to obtain this information offers a cheaper, timely, and more accurate solution compared to alternative methods, such as manual inspection. This information, in turn, represents an asset to identify potential breeding sites of mosquito larvae, which grow only in shallow water pools. As a significant part of the world's population is affected by mosquito-borne viral infections, including Dengue and Zika, identifying mosquito breeding sites is key to control their spread. Experiments with 5-band drone imagery show that our CNN-based approach is able to measure shallow water depths accurately up to a root mean square error of less than 0.5 cm, outperforming state-of-the-art Random Forest methods and empirical approaches.