A device for packaging and applying a cosmetic or care product includes a container intended to contain the product and having at least one product outlet orifice. An applicator member is connected to the container so as to be in communication with the outlet orifice, and a cap is mounted removably on the container between a position covering the applicator member and a removed position. The cap is able to engage with the applicator member in order to close off the outlet orifice. The device includes a guide for guiding the cap in relation to the container, and configured such that the cap is guided in relation to the container along a translation path extending in at least two different directions.