Development of the laser-driven particle accelerators to produce the proton beams necessary for the nuclear medicine is a rapidly upcoming field. Laser-accelerated proton spectra feature a broad energy spread in comparison with the case of proton beams produced by conventional accelerators. The thin silicon planar p-i-n structures can be used for the diagnostic of such beams due to their real-time readout, compactness and standard fabrication technologies. In the present work, the application of thin silicon planar p-i-n diodes for the proton spectrum determination of the laser-driven proton beams is theoretically investigated. The method of the proton spectrum reconstruction from the temporal response of the detector irradiated with a single laser-driven proton burst for different distances between proton source of the laser-driven accelerator and detector position has been developed. The temporal response of the detector was modeled for the ultra-thin ultra-fast silicon diode.