We use N-body simulations to examine the effects of mass outflows on the density profiles of cold dark matter (CDM) halos surrounding dwarf galaxies. In particular, we investigate the consequences of supernova-driven winds that expel a large fraction of the baryonic component from a dwarf galaxy disk after a vigorous episode of star formation. We show that this sudden loss of mass leads to the formation of a core in the dark matter density profile, although the original halo is modeled by a coreless (Hernquist) profile. The core radius thus created is a sensitive function of the mass and radius of the baryonic disk being blown up. The loss of a disk with mass and size consistent with primordial nucleosynthesis constraints and angular momentum considerations imprints a core radius which is only a small fraction of the original scale-length of the halo. These small perturbations are, however, enough to reconcile the rotation curves of dwarf irregulars with the density profiles of haloes formed in the standard CDM scenario.