Police said 34-year-old Grace Trinidad, who works at New Visions Charter High School for Advanced Math & Science in Spuyten Duyvil, was picked up by police after the principal contacted the teenager's mother.
Detectives believe Trinidad allegedly had sex with the male student at her home.
Trinidad was charged with rape, criminal sex act and unlawful dealing with a child.
New Visions for Public Schools operates eight charter schools in the city.
The school opened in 2011 and enrolls almost 500 students.
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