Device for administering a fluid into a patient's conjunctival sac, which combines in a single product optimum characteristics in terms of stability, positioning and spacing of the fluid dispenser with respect to the surface of the eye, as well as guiding of the dispensed fluid towards the center of the eye. The device has the shape of a hollow truncated cone (1), the minor (top,2) base of which is adapted to house the dropper of a fluid dispenser and the major (bottom,3) base of which has a non-coplanar ovoid shape and is adapted to rest precisely on the periocular area. The device allows safe spacing of the tip of the dripper from the corneal surface, preventing accidental contact between dripper and cornea. The dispensed fluid is directed towards the center of the eye surface, without coming into contact with the device. The device is constructively simple, low-cost and suitable for possible disposable use.