A novel matrix pencil-based interference mitigation approach for FMCW radars is proposed in this paper. The interference-contaminated segment of the beat signal is firstly cut out and then the signal samples in the cut-out region are reconstructed by modeling the beat signal as a sum of complex exponentials and using the matrix pencil method to estimate their parameters. The efficiency of the proposed approach for the interference with different parameters (i.e. interference duration, signal-to-noise ratio (SNR), and different target scenarios) is investigated by means of numerical simulations. The proposed interference mitigation approach is intensively verified on experimental data. Comparisons of the proposed approach with the zeroing and other beat-frequency interpolation techniques are presented. The results indicate the broad applicability and superiority of the proposed approach, especially in low SNR and long interference duration situations.