In this Letter, we propose a dynamic fiber-optic white light interferometry (WLI) based on the compressed-sensing (CS) principle. The time-varying interference spectra of a Fabry-Perot cavity under vibration are considered as a two-dimensional (2D) signal with respect to both laser wavelength and time, which can be compressively sampled using a programmable semiconductor laser source during the measurement process. After CS reconstruction, the spectrum acquisition rate is equal to the random wavelength modulation rate, up to 10 MHz in this Letter, providing an attractive alternative to laser-based dynamic interferometry. Numerical simulations and nanometer-scale vibration experiments verify the effectiveness of the scheme.