Low-frequency noise in 4H-SiC MOSFETs has been measured for the first time. At drain currents varying from deep subthreshold to strong inversion, the 1/f (flicker) noise dominated at frequencies 1 - 105 Hz. The dependence of relative spectral noise density, , on drain current Id (at a constant drain voltage Vd) differs qualitatively from that in Si MOSFETs. In Si MOSFETs, ~ 1/ in strong inversion, whereas tends to saturate in sub-threshold. In 4H-SiC MOSFETs under study, ~ 1/ over the whole range of currents from deep sub-threshold to strong inversion. Similar noise behavior is often observed in poly- or a-Si TFTs. The effective channel mobility in 4H-SiC MOSFETs, 3 - 7 cm2/Vs, is also as low as that in TFTs. Both noise behavior and transport properties of 4H-SiC MOSFETs are explained, analogously to TFTs, by a high density of localized states (bulk and interface) near the conduction band edge in the ion implanted p-well.