Aims. The evolution of dwarf galaxies is dramatically affected by gaseous and dusty outflows, which can easily deprive their interstellar medium of the material needed for the formation of new stars, simultaneously enriching their surrounding circumgalactic medium (CGM). In this Letter, we present the first evidence of extended [CII] 158 μm line and dust continuum emission in local dwarf galaxies hosting star-formation-driven outflows. Methods. By stacking the [CII], far-infrared, and near-UV (NUV) emission obtained from Herschel and GALEX data, we derived the average radial profiles, and compared the spatial extension of gas, dust, and stellar activity in dwarf galaxies. Results. We find that [CII] and dust emissions are comparable to each other, and more extended than the NUV continuum. The [CII] size is in agreement with that measured for z > 4 star-forming galaxies, suggesting that similar mechanisms could be at the origin of the observed atomic carbon reservoir around local and high-z sources. The cold dust follows the [CII] emission, going beyond the stellar continuum as opposed to what is typically observed in the early Universe where measurements can be affected by the poor sensitivity and faintness of dust emission in the CGM of high-z galaxies. Conclusions. We attribute the extended [CII] and dust continuum emission to the presence of galactic outflows. As local dwarf galaxies are considered analogs of primordial sources, we expect that comparable feedback processes can be at the origin of the observed [CII] halos at z > 4, dominating over other possible formation mechanisms.