Deep Frequency Modulation (DFM) interferometry is an effective approach for simplifying laser interferometry systems in space gravitational wave detection. However, the conventional use of kHz-level modulation frequencies in current DFM techniques introduces coupling of laser power noise into the system, which increases background noise and limits the ability to meet the stringent requirements of high-precision space measurements. This paper proposes to increase the DFM modulation frequency to the MHz range to mitigate the effects of laser power noise. Through an in-depth analysis of the DFM technique, we developed a phase signal extraction method for DFM interferometry using Bessel function expansion, orthogonal demodulation, and promotion of J1···J4 method. Based on the signal processing requirements at the MHz-level, the hardware and software architecture of a phase measurement system was developed, followed by extensive testing and evaluation under various operating conditions. The results demonstrate that the phase measurement system exhibits excellent linearity and accuracy, with phase noise in the frequency band from 2 mHz to 1 Hz consistently below 2π µrad/$\sqrt{{\mathrm{Hz}}} $, thus meeting the phase measurement requirements for space-based gravitational wave detection.