To address the complexity and low detection accuracy issues in the intrinsic frequency detection process of fiber optic gyroscopes, a highly precise automatic measurement method based on optimal projection approximation is proposed. Building upon the digital closed-loop fiber optic gyroscope hardware circuit, this method generates a frequency-adjustable square wave with a 25% duty cycle through field-programmable gate array (FPGA) fractional division. Subsequently, it calculates the difference between the high and low levels of the sign bits of the modulated optical intensity signal sampled by the analog-to-digital converter (ADC). This yields an error signal related to the modulation frequency and intrinsic frequency. The modulation frequency is then approximated using the nearest projection of this error signal, thereby achieving automatic detection of the fiber optic gyroscope’s intrinsic frequency. The experimental results indicate that this method, requiring no external auxiliary equipment, enables rapid and highly accurate measurement of the intrinsic frequency of the fiber optic gyroscope. The measurement of intrinsic frequency takes approximately 300 milliseconds, achieving a measurement accuracy of up to 0.001 Hz.