Social sensing has emerged as a pervasive and scalable sensing paradigm to obtain timely information of the physical world from "human sensors". In this paper, we study a new extremely-sparse disaster damage assessment (DBA) problem in social sensing. The objective is to automatically assess the damage severity of affected areas in a disaster event by leveraging the imagery data reported on online social media with extremely sparse training data (e.g., only 1% of the data samples have labels). Our problem is motivated by the limitation of current DDA solutions that often require a significant amount of high-quality training data to learn an effective DDA model. We identify two critical challenges in solving our problem: i) it remains to be a fundamental challenge on how to effectively train a reliable DDA model given the lack of sufficient damage severity labels; ii) it is a difficult task to capture the excessive and fine-grained damage-related features in each image for accurate damage assessment. In this paper, we propose ContrastDDA, a deep contrastive learning approach to address the extremely-sparse DDA problem by designing an integrated contrastive and augmentative neural network architecture for accurate disaster damage assessment using the extremely sparse training samples. The evaluation results on two real-world DDA applications demonstrate that ContrastDDA clearly outperforms state-of-the-art deep learning and semi-supervised learning baselines with the highest DDA accuracy under different application scenarios.