The news agency reported additional rebel fire on other parts of west Aleppo, which is regularly targeted by the opposition forces that hold the eastern part of the divided city.
The Syrian Observatory for Human Rights, a Britain-based monitor, gave a toll of eight children killed, aged between six and 12.
An AFP photographer at the school shortly after the attack saw adults rushing children away from the building and trying to comfort crying infants.
State television showed some of the wounded being treated in a hospital, including a child in a blue top whose face was covered in blood being attended on a stretcher.
In a corridor, a young boy in a red T-shirt with his arm in a make-shift sling was shepherded by his distraught mother, as another boy with his head bandaged was carried in.
Government forces are currently waging a ferocious assault against east Aleppo, targeting it with air strikes, barrel bombs and artillery fire.
They renewed their fire on the east on Tuesday, after a period of relative respite, in a bid to recapture the rebel-held side of the city.
The Observatory says at least 103 civilians have been killed in east Aleppo since government forces resumed the assault.