The woman, speaking on a mobile phone, says that shortly after she left the college for a meeting elsewhere, assailants attacked the school, throwing explosive devices and firing guns.
The committee's spokeswoman, Svetlana Petrenko, said 13 people were killed and about 50 were injured. "It was a fourth year student of this college", Askyonov told state television.
The National Anti-Terrorism Committee said in a statement that the blast at the college, in the city of Kerch in eastern Crimea, was caused by an explosive device.
Emergency officials initially had said the blast was caused by a gas explosion.
Law enforcement officials said they were treating the incident, in which numerous victims were teenage pupils, as a terrorist attack.
Russian President Vladimir Putin said the attack was a tragedy and offered condolences to the victims' families.
But a Russian national guard official said the incident was a deliberate "terrorist act".
Video footage from the scene showed armoured personnel carriers and military tucks lined up on the approach to the college, in the Crimean city of Kerch. The shooter was later identified as Vladislav Roslyakov, who officials said was a local resident. FM showed the ground floor windows of the two-storey building had been blown out and debris was lying on the ground outside.
TASS also quoted medical workers as saying that 18 people had been hospitalized and that they were expecting more injured to be brought in.
Russian Federation unilaterally annexed Crimea from Ukraine in 2014, a move that triggered Western sanctions.
"There are already lots of people in the emergency room, and in the operating theatre", the TASS news agency quoted the employee as saying.
The victims died from gunshot wounds, the agency said.
Kerch is the landing point and namesake of a bridge that opened earlier this year to connect Crimea to Russian Federation.