We report the discovery by the Large Area Telescope (LAT) onboard the Fermi Gamma-ray Space Telescope of high-energy gamma-ray emission from the peculiar quasar PMN J0948+0022 (z=0.5846). The optical spectrum of this object exhibits rather narrow Hbeta (FWHM(Hbeta) ~ 1500 km s^-1), weak forbidden lines and is therefore classified as a narrow-line type I quasar. This class of objects is thought to have relatively small black hole mass and to accrete at high Eddington ratio. The radio loudness and variability of the compact radio core indicates the presence of a relativistic jet. Quasi simultaneous radio-optical-X-ray and gamma-ray observations are presented. Both radio and gamma-ray emission (observed over 5-months) are strongly variable. The simultaneous optical and X-ray data from Swift show a blue continuum attributed to the accretion disk and a hard X-ray spectrum attributed to the jet. The resulting broad band spectral energy distribution (SED) and, in particular, the gamma-ray spectrum measured by Fermi are similar to those of more powerful FSRQ. A comparison of the radio and gamma-ray characteristics of PMN J0948+0022 with the other blazars detected by LAT shows that this source has a relatively low radio and gamma-ray power, with respect to other FSRQ. The physical parameters obtained from modelling the SED also fall at the low power end of the FSRQ parameter region discussed in Celotti & Ghisellini (2008). We suggest that the similarity of the SED of PMN J0948+0022 to that of more massive and more powerful quasars can be understood in a scenario in which the SED properties depend on the Eddington ratio rather than on the absolute power.