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New Jersey police documents said Reddy had sex with the child in River Road Park, earlier this year.
The former Pennington School teacher was arrested on Friday in Baltimore, Maryland, where she now lives.
Reddy was later charged with sexual assault and unlawful contact with a minor.
A trial date has yet to be set.
Reddy is the latest US teacher to be charged with having sex with a pupil.
Daily Star Online reported married educator Hunter Day, 22, was charged with second-degree rape after she allegedly had sex with a student.
When they arrived at her home, Day sent a text to the police, who posed as a pupil, reading: “I’m here, the door’s unlocked as usual.”
Inside, she was found sitting on the living room floor with the lights turned off, candles lit and wearing a Christmas-style top featuring a cat in a Santa Claus hat and workout shoes – police claim.
When detectives quizzed Day, she reportedly admitted to having sex with the pupil.