We report on the first detection of GeV high-energy gamma-ray emission from a young supernova remnant with the Large Area Telescope aboard the Fermi Gamma-ray Space Telescope. These observations reveal a source with no discernible spatial extension detected at a significance level of 12.2$\sigma$ above 500 MeV at a location that is consistent with the position of the remnant of the supernova explosion that occurred around 1680 in the Cassiopeia constellation - Cassiopeia A. The gamma-ray flux and spectral shape of the source are consistent with a scenario in which the gamma-ray emission originates from relativistic particles accelerated in the shell of this remnant. The total content of cosmic rays (electrons and protons) accelerated in Cas A can be estimated as $W_{\mathrm{CR}} \approx (1-4) \times 10^{49}$ erg thanks to the well-known density in the remnant assuming that the observed gamma-ray originates in the SNR shell(s). The magnetic field in the radio-emitting plasma can be robustly constrained as B $\gt 0.1$ mG, providing new evidence of the magnetic field amplification at the forward shock and the strong field in the shocked ejecta.