Young Buck threatened to burn down his ex-girlfriend's apartment ... according to cops in Tennessee.

Law enforcement sources tell us YB was picked up after his ex-gf reported the rapper texted her the threat on Wednesday ... then showed up at her apartment, kicked down the door, but left without disturbing anything inside.

Cops arrested him on Thursday. He was in custody for a few hours before being released on a $5k bond.

We're told Young Buck is currently on federal probation, and this arrest could mean he'll be busted for a violation.