A fluid container for supplying a consuming device with a working fluid, including at least one connector piece having a shut-off valve arranged therein for preventing undesired escaping of the working fluid from the fluid container. In order to increase safety against undesired emptying of the fluid container, it is provided that the valve closure body, in the closed state of the shut-off valve, is accommodated in the fluid container completely inside a contour formed by an outer edge of the connector piece, and provision is made, for support against the valve closure body, of a support, which, upon insertion of the connector piece into the receiving seat, engages at least regionally into the connecting duct and in this way displaces the valve closure body in the connecting duct.