Mr. Braddy was in custody on Wednesday evening and could not be reached for comment. He also faces one count of acting in a manner injurious to a child and one count of sex abuse, according to the police. A conviction on the more serious of the two criminal sexual act charges carries a sentence of up to seven years in prison.

According to his LinkedIn profile, Mr. Braddy has taught eighth-grade math and advanced Algebra I at the school at 100-01 Flatlands Avenue since September 2015.

In a statement, Douglas Cohen, a spokesman for the city Department of Education, said, “These deeply disturbing allegations have no place in our schools.” He said that Mr. Braddy was immediately removed from the school and “will remain away from students pending the outcome of the investigation and we will pursue his removal from payroll as soon as legally possible.”

On Twitter, Mr. Braddy goes by the username OFFICER_friskHer and describes himself as a college graduate who loves numbers and music.

Mr. Braddy also said on LinkedIn that he is an adjunct lecturer at the City University of New York.

For nearly three years until May 2014, he worked as a teaching assistant at the university’s Research Foundation and Medgar Evers College in Crown Heights.