Fingerprint spectral response of several materials with terahertz electromagnetic radiation indicates that terahertz technology is an effective tool for sensing applications. However, sensing few nanometer thin-film of dielectrics with much longer terahertz waves (1 THz = 0.3 mm) is challenging. Here, we demonstrate a quasi-bound state in the continuum (BIC) resonance for sensing of nanometer scale thin analyte deposited on a flexible metasurface. The large sensitivity originates from strong local field confinement of the quasi-BIC Fano resonance state and extremely low absorption loss of a low-index cyclic olefin copolymer substrate. A minimum thickness of 7 nm thin-film of germanium is sensed on the metasurface, which corresponds to a deep subwavelength length scale of {lambda}/43000, where {lambda} is the resonance wavelength. The low-loss, flexible and large mechanical strength of the quasi-BIC micro structured metamaterial sensor could be an ideal platform for developing ultrasensitive wearable terahertz sensors.