maxillary artery ma·xil·la·ryartery uncommon noun 1. either of two arteries branching from the external carotid artery and supplying structure of the face Synonymsmaxillary arteryarteria maxillaris Related words Broader terms artery Narrower terms facial arteryinternal maxillary artery WordNet 2.1 (Princeton University). WordNet 2.1 Copyright Princeton University. All rights reserved.