Classification of texts by genre is an important application of natural language processing to literary corpora but remains understudied for premodern and non-English traditions. We develop a stylometric feature set for ancient Greek that enables identification of texts as prose or verse. The set contains over 20 primarily syntactic features, which are calculated according to custom, language-specific heuristics. Using these features, we classify almost all surviving classical Greek literature as prose or verse with >97% accuracy and F1 score, and further classify a selection of the verse texts into the traditional genres of epic and drama.