It happened just before 1 p.m. at the Walton High School in the Kingsbridge Heights section.
The victim was said to be alert and conscious when he was taken to Jacobi Hospital.
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The 15-year-old suspect was taken to the principal's office and held for police.
The weapon was an unknown sharp object, though it may have been a pair of scissors.
Walton Campus is a scanning school with a full complement of school safety agents.
"Safety is our top priority, and NYPD and EMS immediately responded to an incident on the Walton Campus today," the Department of Education said in a statement. "The student is in stable condition, and we will provide the school with additional safety and counseling support, as well as work closely with NYPD on their investigation."
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