Experimental measurements and a thermodynamic model reveal that nematic elasticity can induce lateral phase separation of amphiphilic molecules assembled at interfaces between thermotropic liquid crystals (LCs) and immiscible aqueous phases. The morphologies of the phase-separated domains of amphiphiles induced by nematic elasticity are shown to be strongly dependent on the nature of the deformation of the LC. This study provides important insight into the physics that controls the ordering of molecules at interfaces of soft anisotropic materials, and identifies a new mechanism of phase separation at these interfaces.