'Hunger Games' Star Josh Hutcherson -- The Mystery of the Broken Nose

With his face bruised and bandaged up, "Hunger Games" star Josh Hutcherson was spotted leaving a doctor's office in Beverly Hills on Monday ... after suffering a mysterious injury to his nose.

Hutcherson first tweeted about the injury on May 9th ... saying, "Just had surgery to fix my broken nose" ... and later his rep told us the actor had been diagnosed with a deviated septum.

But there's one big question -- how DID the 19-year-old movie star break his nose?

Josh isn't saying ... and neither is his rep ... who told TMZ "no further details will be released."