To respond to disasters such as earthquakes, wildfires, and armed conflicts, humanitarian organizations require accurate and timely data in the form of damage assessments, which indicate what buildings and population centers have been most affected. Recent research combines machine learning with remote sensing to automatically extract such information from satellite imagery, reducing manual labor and turn-around time. A major impediment to using machine learning methods in real disaster response scenarios is the difficulty of obtaining a sufficient amount of labeled data to train a model for an unfolding disaster. This paper shows a novel application of semi-supervised learning (SSL) to train models for damage assessment with a minimal amount of labeled data and large amount of unlabeled data. We compare the performance of state-of-the-art SSL methods, including MixMatch and FixMatch, to a supervised baseline for the 2010 Haiti earthquake, 2017 Santa Rosa wildfire, and 2016 armed conflict in Syria. We show how models trained with SSL methods can reach fully supervised performance despite using only a fraction of labeled data and identify areas for further improvements.