1. A three-dimensional (3D) space interface apparatus comprising: a 3D display unit to output a 3D virtual object; a sensing unit to generate a sensing signal for sensing a position and a movement of a user and for sensing a position and a movement of a manipulation object; and an interface unit to verify, using the sensing signal, whether a predetermined movement of the manipulation object has occurred or whether a contact between the 3D virtual object and the manipulation object has been made, and to generate a predetermined reaction corresponding to the predetermined movement or the contact.