An engine mount apparatus may include a mount housing which has an internal space; a partition device which partitions the internal space into an upper space and a lower space; a nozzle plate which is provided in the upper space and allows a fluid to selectively pass through the nozzle plate; an upper diaphragm which is fastened to an upper surface of the nozzle plate and defines an upper liquid chamber; a core which penetrates the partition device, and has an upper portion disposed in the upper space, and a lower portion disposed in the lower space; a lower diaphragm which extends from the upper portion of the core to a lower surface of the nozzle plate, and defines a lower liquid chamber; and a rubber member which is provided in the upper space, and connects the upper portion of the core and the partition device.