Its ability to uniformly observe the sky coupled with its very high sensitivity and very good angular resolution, make the Fermi Large Area Telescope (LAT) well suited for searching for exotic gamma-ray signals in the 20 MeV to over 300 GeV energy range. Dark Matter is strongly believed to compose about one fourth of the total energy of the Universe. Its unknown nature is one of the most intriguing questions in present day cosmology. Several scenarios beyond the Standard Model of particle physics predict that weakly interacting massive particles composing this non-baryonic matter can produce an observable continuum of high-energy gamma rays from their annihilation or decay. Indirect searches for dark matter signals have been conducted with the first 11 months of observation of dwarf spheroidal galaxies. These objects, the largest galactic clumps of dark matter known, are expected to be free from conventional gamma-ray sources and have very low content of gas and dust, making them some of the most promising targets for dark matter searches. An overview of the search for a gamma-ray signal in dwarf spheroidal galaxies, conducted with the LAT, will be presented. Constraints obtained on specific dark matter models will also be shown.