State news agency SANA said the “terrorist attack” on Thursday hit the school in the al-Suleimaniya area in western Aleppo.
The so-called Syrian Observatory for Human Rights, which is sympathetic to militants, confirmed the shelling.
Terrorists also fired rockets into al-Manshia, Sheikh Taha and Bustan al-Basha neighborhoods of Aleppo, killing five people and injuring 13 others.
According to the United Nations, more than 100 children have been killed since a US- and Russian-brokered truce collapsed on Sept. 19.
Aleppo has been divided between government and militant control for years but the army has mounted an offensive recently to drive out terrorists.
On Thursday, Syrian troops attacked militant positions in northwest Aleppo as warplanes carried out sorties.
On the northeastern outskirts of the city, advancing army troops captured several hilltops overlooking terrorist-held areas.
Government forces plan to send special troops to seize control of the areas which are currently controlled by militants.
The Halab Today TV channel, run by militants, reported "intense" airstrikes on terrorist-held parts of Aleppo.
The Syrian government launched the assault to capture all of Aleppo last month after the ceasefire collapsed.
Officials said on Wednesday US Secretary of State John Kerry will meet his Russian counterpart Sergei Lavrov in Switzerland on Saturday to discuss Syria.
The meeting was expected to include foreign ministers from Turkey, Qatar, Saudi Arabia and Iran.
The Kremlin said President Vladimir Putin spoke to French President Francois Hollande and German Chancellor Angela Merkel on Wednesday and said he hoped Saturday's talks would be "fruitful".
Putin later told France's TF1 television channel that the West, especially the US, is responsible for Syria's plight and dismissed the Western accusations of war crimes as "political rhetoric".
The Syrian army has gained the upper hand in the Aleppo battle, prompting accusations by the West that civilians were being targeted in the offensive.
The US pressured Russia into accepting a ceasefire deal last month as Syrian troops pushed into a strategic corner of Aleppo under the militant control.
US warplanes later attacked Syrian army positions in Deir Ezzor, killing 83 soldiers.
The United States also failed to implement an important plank of the ceasefire deal which was to separate militants from al-Nusra Front terrorists.
Kerry broke off talks with Lavrov last week over the offensive. The Syrian and Russian governments blamed the US for breaking the ceasefire, Press TV reported.
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