An MHD vibration sensor, as a new type of sensor used for vibration measurements, meets the technical requirements for the low-noisy measurement of acceleration, velocity, and micro-vibration in spacecraft during their development, launch, and orbit operations. A linear vibration sensor with a runway type based on MHD was independently developed by a laboratory. In a practical test, its output signal was mixed with a large amount of noise, in which the continuous narrowband interference was particularly prominent, resulting in the inability to efficiently carry out the real-time detection of micro-vibration. Considering the high interference of narrowband noise in linear vibration signals, a single-channel blind signal separation method based on SSA and FastICA is proposed in this study, which provides a new strategy for linear vibration signals. Firstly, the singular spectrum of the linear vibration signal with noise was analyzed to suppress the narrowband interference in the collected signal. Then, a FastICA algorithm was used to separate the independent signal source. The experimental results show that the proposed method can effectively separate the useful linear vibration signals from the collected signals with low SNR, which is suitable for the separation of the MHD linear vibration sensor and other vibration measurement sensors. Compared with EEMD, VMD, and wavelet threshold denoising, the SNR of the separated signal is increased by 10 times on average. Through the verification of the actual acquisition of the linear vibration signal, this method has a good denoising effect.