During natural disasters, people often use social media platforms, such as Twitter, to post information about casualties and damage produced by disasters. This information can help relief authorities gain situational awareness in nearly real time, and enable them to quickly distribute resources where most needed. However, annotating data for this purpose can be burdensome, subjective and expensive. In this paper, we investigate how to leverage the copious amounts of unlabeled data generated on social media by disaster eyewitnesses and affected individuals during disaster events. To this end, we propose a semi-supervised learning approach to improve the performance of neural models on several multimodal disaster tweet classification tasks. Our approach shows significant improvements, obtaining up to 7.7% improvements in F-1 in low-data regimes and 1.9% when using the entire training data. We make our code and data publicly available at https://github.com/iustinsirbu13/multimodal-ssl-for-disaster-tweet-classification.