The infraorbital artery is an artery in the head that branches off the maxillary artery, emerging through the infraorbital foramen, just under the orbit of the eye.Diagram showing the origins of the main branches of the carotid arteries.Bloodvessels of the eyelids, front view.ocular group: central retinal The infraorbital artery is an artery in the head that branches off the maxillary artery, emerging through the infraorbital foramen, just under the orbit of the eye. The infraorbital artery appears, from its direction, to be the continuation of the trunk of the maxillary artery, but often arises in conjunction with the posterior superior alveolar artery. It runs along the infraorbital groove and canal with the infraorbital nerve, and emerges on the face through the infraorbital foramen, beneath the infraorbital head of the levator labii superioris muscle.