In this paper, we propose a novel algorithm to extrinsically calibrate a camera to a 3D reference object that is not directly visible from the camera. We use the spherical human cornea as a mirror and calibrate the extrinsic parameters from its reflection of the reference points. The key contribution of this paper is to present a cornea-reflection-based calibration algorithm with minimal configuration; there are three reference points and one mirror pose. The proposed algorithm introduces two constraints. First constraint is that the cornea is virtually a sphere, which enables us to estimate the center of the cornea sphere from its projection. Second is the equidistance constraint, which enables us to estimate the 3D position of the reference point by assuming that the center of the camera and reference point are located the same distance from the center of the cornea sphere. We demonstrate the advantages of the proposed method with qualitative and quantitative evaluations using synthesized and real data.