We present an accurate model of the muon-induced background in the DAMA/LIBRA experiment. Our work challenges proposed mechanisms which seek to explain the observed DAMA signal modulation with muon-induced backgrounds. Muon generation and transport are performed using the MUSIC/MUSUN code, and subsequent interactions in the vicinity of the DAMA detector cavern are simulated with Geant4. We estimate the total muon-induced neutron flux in the detector cavern to be Φ(n)(ν)=1.0 × 10(-9) cm(-2) s(-1). We predict 3.49 × 10(-5) counts/day/kg/keV, which accounts for less than 0.3% of the DAMA signal modulation amplitude.