The problem of designing a fast and accurate image reconstruction algorithm for 3-D near-field microwave imaging with sparse multiple-input multiple-output (MIMO) arrays is discussed in this article. Time-domain reconstruction algorithms, including the backprojection algorithm (BPA) and the Kirchhoff migration algorithm (KMA), have impractically high-computational costs, and wavenumber domain algorithms, including range migration algorithms (RMAs), are challenging to develop for generic nonuniform ultrasparse MIMO arrays. Based on the fast factorized BPAs for synthetic aperture radar (SAR) imaging, the fast factorized KMA (FFKMA) is proposed. Local spectrum properties of near-field radar images are modeled and exploited to ensure efficient sampling of the subimages in near-field MIMO settings. The proposed algorithm achieves imaging quality close to that of KMA and comparable computational efficiency of fast Fourier transform-based RMAs, while still applicable to generic sparse MIMO arrays. Finally, the algorithm is verified with numerical simulations and experiments.