Background In order to understand public sentiment regarding the Zika virus, social media can be leveraged to understand how positive, negative, and neutral sentiments are expressed in society. Specifically, understanding the characteristics of negative sentiment could help inform federal disease control agencies' efforts to disseminate relevant information to the public about Zika related issues. Objective The purpose of this study was to analyze public sentiment concerning Zika using posts on Twitter and determine the qualitative characteristics of positive, negative and neutral sentiments expressed. Methods Machine learning techniques and algorithms were used to analyze the sentiment of tweets concerning Zika. A supervised machine learning classifier was built to classify tweets into three sentiment categories: positive, neutral, and negative. Tweets in each category were then examined using a topic modeling approach in order to determine the main topics for each category, with focus on the negative category. Results A total of 5,303 tweets were manually annotated and used to train multiple classifiers. These performed moderately well (F1 score = 0.69, 0.68) with text-based feature extraction. All 48,734 tweets were then categorized into the sentiment categories. Ten topics for each sentiment category were identified using topic modeling with a focus on the negative sentiment category. Conclusions Our study demonstrates how sentiment expressed within discussions of epidemics on Twitter can be discovered. This allows public health officials to understand public sentiment regarding an epidemic and enables them to address specific elements of negative sentiment in real-time. Our negative sentiment classifier was able to identify tweets concerning Zika with three broad themes: neural defects, Zika abnormalities, and reports and findings. These broad themes were based on domain expertise and from topics discussed in journals such as MMWR and Vaccine. Since the majority of topics in the negative sentiment category concerned symptoms, officials should focus on spreading information about prevention and treatment research.