A wiping device for a fluid product applicator including a first part forming a support, a second part forming a wiping sleeve, the wiping sleeve making it possible to wipe an applicator stick immersing in a liquid product, the first part forming a support including an annular base resting on a mouth of the container, with an axial bearing collar and a tubular portion, the second part forming a wiping sleeve including a central passage and a wiping lip, with a plurality of legs extending from the annular base towards the sleeve, the legs being separated by secondary passages, which are located radially outside the sleeve and radially inside the tubular portion of the base, with an upper wiping lip having a free edge arranged in a plane located in the vicinity of the upper plane of the collar of the base.