A device for dispensing a fluid product, comprising a body, a slit stopper formed in the body, being made from an elastically deformable material and delimited by an external face and an internal face, the slit stopper comprising a slit approximately parallel to the principal plane of the device, that extends from the internal face to the external face, and that comprises two facing walls that bear in contact with each other and that can move apart following a movement perpendicular to the principal plane of the device under pressure from the product to be dispensed, by elastic strain of the slit stopper. The slit stopper comprises a groove made in the internal face, that comprises two inclined faces each of which prolongs a wall of the slit in the inwards direction. The device may include a layer of material with bactericide or bacteriostatic properties on its external face.