The flux of gamma rays with energies >100MeV is dominated by diffuse emission from CRs illuminating the ISM of our Galaxy through the processes of Bremsstrahlung, pion production and decay, and inverse-Compton scattering. The study of this diffuse emission provides insight into the origin and transport of CRs. We searched for gamma-ray emission from the SMC in order to derive constraints on the CR population and transport in an external system with properties different from the Milky Way. We analysed the first 17 months of continuous all-sky observations by the Large Area Telescope of the Fermi mission to determine the spatial distribution, flux and spectrum of the gamma-ray emission from the SMC. We also used past radio synchrotron observations of the SMC to study the population of CR electrons specifically. We obtained the first detection of the SMC in high-energy gamma rays, with an integrated >100MeV flux of (3.7 +/-0.7) x10e-8 ph/cm2/s, with additional systematic uncertainty of <16%. The emission is steady and from an extended source ~3{\deg} in size. It is not clearly correlated with the distribution of massive stars or neutral gas, nor with known pulsars or SNRs, but a certain correlation with supergiant shells is observed. The observed flux implies an upper limit on the average CR nuclei density in the SMC of ~15% of the value measured locally in the Milky Way. The population of high-energy pulsars of the SMC may account for a substantial fraction of the gamma-ray flux, which would make the inferred CR nuclei density even lower. The average density of CR electrons derived from radio synchrotron observations is consistent with the same reduction factor but the uncertainties are large. From our current knowledge of the SMC, such a low CR density does not seem to be due to a lower rate of CR injection and rather indicates a smaller CR confinement volume characteristic size.< Réduire