Christian Toro, 27, is accused of paying students from his former school to take fireworks apart to get gunpowder, officials said on Thursday.
His twin brother Tyler is also in custody. The FBI investigated a bomb threat against the school in December.
“Neither of these two individuals were on our radar before this, nor did they have any criminal background,” said John Miller, New York’s counter-terrorism deputy commissioner in a late-night news conference.
Mayor Bill de Blasio also reassured citizens that there was “no imminent threat directed at New York City at this time”.
Christian Toro was a high school teacher in Manhattan’s Harlem neighborhood when a bomb threat was made on 4 December 2017 to his school. One student was arrested and Mr Toro resigned from his teaching position.
School staff later discovered instructions for manufacturing explosive devices on his work laptop which his brother Tyler, 27, had returned on his behalf.
Following a search of the brothers’ shared apartment in the Bronx district, the FBI found a stockpile of iron oxide, aluminum powder, potassium nitrate and other bomb components including a jar containing explosive powder and metal spheres.
At least two students from the school had visited the home, where Christian Toro paid them $50 (£35) an hour to break up fireworks and transfer the gunpowder they had extracted into containers, prosecutors said.
Law enforcement agents also found a backpack with a diary notated with the words “Operation Flash” and an index card saying “Under the full moon the small ones will know terror”.
Officials said that the full meaning of these materials was still unclear.
Both brothers were charged in a federal court in Manhattan with unlawfully manufacturing a destructive device, which carries a maximum sentence of 10 years in prison.
Christian Toro is also charged with distributing explosive materials to a minor, also punishable by up to 10 years.