An unusual volume contribution of exchange-coupling-induced uniaxial anisotropy in a single-crystalline Fe/CoO/MgO(001) system was discovered and measured using the magneto-optical Kerr effect. The observed volume contribution emerges with the establishment of CoO antiferromagnetic order below the CoO blocking temperature or above a critical CoO thickness. It decays with decreasing exchange coupling strength tuned by inserting a MgO layer between the Fe and CoO layers. The volume anisotropy of the Fe layer is attributed to the strain transferred from the CoO layer induced by the magnetostriction effect through a field cooling process. Our results indicate that the strain in antiferromagnetic film can be applied to control the exchange coupling effect in the future spintronics devices.