Social media services such as Twitter are valuable sources of information for surveillance systems. A digital syndromic surveillance system has several advantages including its ability to overcome the problem of time delay in traditional surveillance systems. Despite the progress made with using digital syndromic surveillance systems, the possibility of tracking avian influenza (AI) using online sources has not been fully explored. In this study, a Twitter-based data analysis framework was developed to automatically monitor avian influenza outbreaks in a real-time manner. The framework was implemented to find worrisome posts and alerting news on Twitter, filter irrelevant ones, and detect the onset of outbreaks in several countries. The system collected and analyzed over 209,000 posts discussing avian influenza on Twitter from July 2017 to November 2018. We examined the potential of Twitter data to represent the date, severity and virus type of official reports. Furthermore, we investigated whether filtering irrelevant tweets can positively impact the performance of the system. The proposed approach was empirically evaluated using a real-world outbreak-reporting source. We found that 75% of real-world outbreak notifications of AI were identifiable from Twitter. This shows the capability of the system to serve as a complementary approach to official AI reporting methods. Moreover, we observed that one-third of outbreak notifications were reported on Twitter earlier than official reports. This feature could augment traditional surveillance systems and provide a possibility of early detection of outbreaks. This study could potentially provide a first stepping stone for building digital disease outbreak warning systems to assist epidemiologists and animal health professionals in making relevant decisions.