We propose a rapid tomographic vibrometer technique using an optical comb to measure internal vibrations, transient phenomena, and tomographic distributions in biological tissue and microelectromechanical system devices at high frequencies. This method allows phase-sensitive tomographic measurement in the depth direction at a multi-MHz scan rate using a frequency-modulated broadband electrooptic multi-GHz supercontinuum comb. The frequency spacing was swept instantaneously in time and axisymmetrically about the center wavelength via a dual-drive Mach-Zehnder modulator driven by a variable radio frequency signal. This unique sweeping method permits direct measurement of fringe-free interferometric amplitude and phase with arbitrarily changeable measurement range and scan rate. Therefore, a compressive measurement can be made in only the depth region where the vibration exists, reducing the number of measurement points. In a proof-of-principle experiment, the interferometric amplitude and phase were investigated for in-phase and quadrature phase-shifted interferograms obtained by a polarization demodulator. Tomographic transient displacement measurements were performed using a 0.12 mm thick glass film and piezo-electric transducer oscillating at 10-100 kHz with scan rates in the range 1-20 MHz. The depth resolution and precision of the vibrometer were estimated to be approximately 25 µm and 1.0 nm, respectively.