The Mona Lisa became world-famous because it was stolen.
On 21 August 1911 Louvre employee Vincenzo Peruggia hid in a broom closet and carried the painting out under his coat after closing time. It sat in his flat for two years. Before 1911 the picture was barely known to the wider public; the manhunt made it a global star. On 4 January 1914 it hung in the Louvre again.
Useful: Fame is often an event rather than a property – paintings included.
Source: en.wikipedia.org