"Fourteen citizens were killed and 86 others wounded by terrorists who targeted the Shaghur neighbourhood in Damascus with four mortar shells," the SANA news agency said, adding that two shells hit the Badr al-Din al-Hussein institute.
The Syrian government and media use the term "terrorists" for all those seeking to overthrow President Bashar al-Assad's government.
The institute is reportedly an Islamic law centre where students from Syria and abroad study religious jurisprudence.
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The Syrian Observatory for Human Rights also reported the mortar attack, saying the toll was higher, with 17 people killed.
The Britain-based monitoring group said the death toll could rise as some of the injured were in critical condition.
Observatory director Rami Abdel Rahman told AFP that the institute taught students as young as 14, but it was not immediately clear if there were children among the dead or wounded.
Rebel forces arrayed in positions on the outskirts of the capital regularly fire mortar shells and rockets into the heart of Damascus, often killing civilians.
Shaghur is a district in the Old City of Damascus, which has been hit by rebel fire frequently.
