The suspect, identified as 23-year-old Prodromos Vasilopoulos, was passing through security at Terminal 4, en route to Greece, when he was stopped at around 8:15 a.m. Wednesday, according to officials.
Vasilopoulos was reportedly caught with a stun gun still in his possession. The weapon, believed to be have been used in the attack, was in a carry-on bag. Screeners at the airport had apparently missed it.
Authorities say he pretended to be a UPS deliveryman to gain entrance Tuesday to the 19-year-old woman's apartment, where he allegedly beat and raped her.
Vasilopoulos was to be arraigned Thursday on various charges, including predatory sexual assault and criminal possession of a weapon.
If convicted, he faces up to 25 years to life in prison.