The Soil Moisture and Ocean Salinity (SMOS) mission led by the European Space Agency (ESA) is aimed at globally monitoring the Earth surface moisture and ocean salinity. As the single payload of the SMOS satellite, the Microwave Interferometric Radiometer with Aperture Synthesis (MIRAS) operates in the protected L-band. Nevertheless, the artificial sources emitting close to or/and entirely in this band are contaminating the collected remote sensing data and deteriorating the performance of the SMOS mission. In this article, we propose a method based on interpolation-assisted matrix completion (IMC) for the localization of RFI sources. The method firstly constructs the augmented covariance matrix (ACM). Secondly, it exploits the local property of visibility function sampling data in the spatial-frequency domain and adopts a local polynomial regression model to interpolate missing visibility data. Thirdly, it exploits the low-rank property of the ACM and recovers this ACM via the matrix completion technique. Finally, the subspace-based algorithm (i.e., MUSIC) is used to estimate source direction-of-arrivals (DOAs) for RFI localization. The proposed RFI localization method is termed as IMC-MUSIC. It is mainly devised for application scenarios where there exist data loss due to inherent array geometry constraint or potential hardware failure and compressed measurements are adopted for reducing system complexity. Validation results show that compared with traditional methods such as discrete Fourier transform (DFT) inversion and covariance-based DOA estimation, the proposed method shows better localization accuracy for different data loss or compression ratios.