We report on gamma-ray observations of the supernova remnant ( SNR ) RX J0852.0 - 4622 with the Large Area Telescope ( LAT ) aboard the Fermi Gamma-ray Space Telescope . In the Fermi LAT data , we find a spatially extended source at the location of the SNR . The extension is consistent with the SNR size seen in other wavelengths such as X-rays and TeV gamma rays , leading to the identification of the gamma-ray source with the SNR . The spectrum is well described as a power law with a photon index of \Gamma = 1.85 \pm 0.06 ~ { } { ( stat ) } ^ { +0.18 } _ { -0.19 } ~ { } { ( sys ) } , which smoothly connects to the H.E.S.S . spectrum in the TeV energy band . We discuss the gamma-ray emission mechanism based on multiwavelength data . The broadband data can be fit well by a model in which the gamma rays are of hadronic origin . We also consider a scenario with inverse Compton scattering of electrons as the emission mechanism of the gamma rays . Although the leptonic model predicts a harder spectrum in the Fermi LAT energy range , the model can fit the data considering the statistical and systematic errors .