The accident happened near the intersection of South 6th Avenue and West 1st Street just before 8 p.m.
Police say the 20-year-old woman swerved to avoid hitting a kid riding a bicycle, hit a metal grate fence and went through it.
The Jeep Cherokee fell to the tracks below and landed on its side, just narrowly missing the electrified third rail.
Three Good Samaritans rushed to help and freed the woman from her car's sun roof.
She was taken to the hospital with minor injuries.
Metro North's New Haven line service was temporarily suspended in both directions, but is running with normal service on Tuesday.