Move it to a separate room, install turnstiles that limit the amount of people in the room to something reasonable, and it will be a better experience for everyone. Even the people who are only there to take a picture of the Mona Lisa will be able to do it faster.
Many other museums seem better at limiting the amount of people near some attraction. To see Da Vinci's next most famous work, The Last Supper, you purchase a ticket that corresponds to a 15-minute slot. The Bust of Nefertiti, one of the most famous antique items, is kept in a separate room of the Neues Museum, with the staff not letting people in if it gets too crowded.