Abstract : The Hausdorff-Young inequality was generalized to locally compact groups by R. Kunze in the unimodular case and then by M. Terp in the general case. A version of this inequality was given by B. Russo for integral operators. In this thesis, we establish a Hausdorff-Young inequality for measured groupoids which covers these results. As in the case of non commutative groups, we make use of the non commutative integration theory. Most of our work is devoted to the identification of the Lp spaces of the von Neumann algebra of the measured groupoid in the cases p=1, 2 as function spaces but also as spaces of random operators.