Social media analysis, such as the analysis of tweets, is a promising research topic for tracking public health concerns including epidemics. In this paper, we present an ontology-based approach to automatically identify public health-related Turkish tweets. The system is based on a public health ontology that we have constructed through a semi-automated procedure. The ontology concepts are expanded through a linguistically motivated relaxation scheme as the last stage of ontology development, before being integrated into our system to increase its coverage. The ultimate lexical resource which includes the terms corresponding to the ontology concepts is used to filter the Twitter stream so that a plausible tweet subset, including mostly public-health related tweets, can be obtained. Experiments are carried out on two million genuine tweets and promising precision rates are obtained. Also implemented within the course of the current study is a Web-based interface, to track the results of this identification system, to be used by the related public health staff. Hence, the current social media analysis study has both technical and practical contributions to the significant domain of public health.