Current sensors are the important component for system control and state monitoring in PV systems. However, due to the influence of operation environment, the current sensor performance degradation often occurs, which affects the operation safety of the system. To detect and estimate the current sensor incipient faults, a novel incipient fault detection and estimation method based on instantaneous amplitude is proposed. Firstly, the incipient fault model of a current sensor based on instantaneous amplitude is established, and the Hilbert transform (HT) algorithm is utilized to estimate instantaneous amplitudes of the three-phase currents, which makes the sinusoidal current signal transformed into the three-dimensional direct current signal. Then the fast moving window principle component analysis (FMWPCA) is used to extract the features of the data matrix composed by the three-dimensional direct current signal, and the probability density distribution functions of principal components and residual subspace vectors are obtained. Subsequently, the Kullback-Leibler (KL) divergence is used to quantitatively measure the small change of actual operation data distribution relative to fault free operation data. Based on above, the fault detection threshold is set and the theoretical model of fault amplitude estimation is constructed to realize the incipient fault detection and estimation of current sensors. Finally, the effectiveness of the proposed method is verified by the RT-LAB platform.