Human-machine co-driving is the main driving mode in the currently automated driving stage. The driver's state has a direct impact on the takeover behavior during co-driving. Therefore, this article considers the effect of driver fatigue on takeover performance based on human-machine co-driving simulation experiments. The experimental time was divided into three periods: morning, afternoon, and evening. The subjective evaluation was used to collect the driver's fatigue values during the experiment. The data was processed by mean calculation, T-test, and interpolation fitting. It was indicated that there has a significant correlation between takeover reaction time and fatigue data through the value of correlation coefficient ($\rho {_(X,Y)} = 0.9$). Takeover reaction time was chosen as the indicator to represent takeover performance. The threshold of takeover reaction time should not exceed 3.3 s in the afternoon and 4.2 s in the evening through the analysis of the effect of driver fatigue on takeover performance. This study can provide theoretical support for the threshold setting of takeover reaction time in the future research of human-machine co-driving.