We report on the effect of forward current stress on the low frequency noise in the 4H–SiC rectifier p+-n diodes rated at 20 and 10 kV. The 4H–SiC diodes with 20 kV blocking voltage were the most sensitive to the forward current stress. Even the stress by the current density j=13 A/cm2 for 30 min led to a noticeable increase in the forward voltage drop and changes in the noise spectra. The stress decreased the level of the 1/f noise but led to the appearance of the burst noise. Stress at higher current densities (50 A/cm2) led to the disappearance of the burst noise and to a further increase in the forward voltage drop. Diodes with 10 kV blocking capability were more resistant to the forward current stress. However, they also demonstrated a decrease in the 1/f noise as a result of the 60 min stress at j=100 A/cm2.