UV-completions of quantum field theories (QFT's) based on string-inspired nonlocality have been proposed to improve the high-energy behavior of local QFT, with the hope of including gravity. One problematic issue is how to realize spontaneous symmetry breaking without introducing an infinite tower of ghosts in the perturbative spectrum. In this letter, a weakly nonlocal extension of the Standard Model (SM) is proposed: the Fuzzy Standard Model (FSM). It is a smooth deformation of the SM based on covariant star-products of fields. This new formalism realizes electroweak symmetry breaking without ghosts at tree-level, and it does not introduce any new elementary particles. We argue that the FSM has several appealing theoretical and phenomenological features that deserve to be investigated in future works.