A woman was raped by a stranger after falling asleep on a subway train in Brooklyn, police said.

The 25-year-old Brooklyn resident told police she was riding the F train around 12:30 a.m. Wednesday when she drifted off — and awoke sometime later to find the man sexually assaulting her.

The victim got off the train, leaving her attacker behind, at the Avenue I station near McDonald Avenue in Midwood. She was taken to a nearby hospital, where a rape kit was conducted, police and law enforcement sources said.

The woman reported her rape to a police precinct around 2 p.m. Wednesday, cops said.

The NYPD’s Special Victims Division is investigating the incident. The attacker is still on the loose.