Millimeter-wave interferometric synthetic aperture radiometer (InSAR) can provide high-resolution observations for many applications by using small antennas to achieve very large synthetic aperture. However, reconstruction of a millimeter-wave InSAR image has been proven to be an ill-posed inverse problem that degrades the performance of InSAR imaging. In this paper, a novel millimeter-wave InSAR image reconstruction approach, referred to as InSAR-TVMC, by total variation (TV) regularized matrix completion (MC) in two-dimensional data space, is proposed. Based on the a priori knowledge that natural millimeter-wave images statistically hold the low-rank property, the proposed approach represents the object images as low-rank matrices and formulates the data acquisition of InSAR in two-dimensional data space directly to undersample visibility function samples. Subsequently, using the undersampled visibility function samples, the optimal solution of the InSAR image reconstruction problem is obtained by simultaneously adopting MC techniques and TV regularization. Experimental results on simulated and real millimeter-wave InSAR image data demonstrate the effectiveness and the significant improvement of the reconstruction performance of the proposed InSAR-TVMC approach over conventional and one-dimensional sparse InSAR image reconstruction approaches.