We report the detection of GeV gamma -ray emission from the supernova remnant (SNR) Puppis A with the Fermi Gamma-Ray Space Telescope. Puppis A is among the faintest SNRs yet detected at GeV energies, with a luminosity of only 2.7 x 10 super(34) (D/2.2 kpc) super(2) erg s super(-1) between 1 and 100 GeV. The gamma -ray emission from the remnant is spatially extended, with a morphology matching that of the radio and X-ray emission, and is well described by a simple power law with an index of 2.1. We attempt to model the broadband spectral energy distribution (SED), from radio to gamma -rays, using standard nonthermal emission mechanisms. To constrain the relativistic electron population we use 7 years of Wilkinson Microwave Anisotropy Probe data to extend the radio spectrum up to 93 GHz. Both leptonic- and hadronic-dominated models can reproduce the nonthermal SED, requiring a total content of cosmic-ray electrons and protons accelerated in Puppis A of at least W sub(CR) approximately (1-5) x 10 super(49) erg.