A sharps container for only one medical pen needle is configured with an elongated, hollow shield having an axially extending recess at a first end thereof. The recess is sized to receive the outer diameter of a pen needle hub. A cover member, sized for closing off the first end of the shield, is connected to the shield by means facilitating movement of the cover member between (i) a first position adjacent to a side of the shield and (ii) a second position abutting the first end of the shield. Locking means may be used for locking the cover member in the second position. The container has dual utilizations, first as a container for only one used medical pen needle and alternatively as a container for only one unused medical pen needle.