Twenty - six people were also wounded when mortar shells fell outside the historic Umayyad Mosque, reported the state - run news agency SANA, citing police.
The agency said the attack had been carried out by foreign backed terrorist groups.
The attack comes a day after a mortar shelling of the Russian embassy in Damascus, which killed one person and wounded nine.
Earlier on Thursday, foreign - backed militants also fired mortar shells into Idlib University in northwest Syria, killing two people, including one student, and injuring 17 others.
The Thursday’s attacks came as the Syrian army recaptured the town of Deir Attiyeh in Qalamoun area earlier in the day. The town links Damascus to the western city of Homs.
Syria ' s crisis began in March 2011 with anti - government protests that were put down violently.
Since then, various rebel groups have been engaged in a multiple - front war with government troops.
The UN estimates that more than 100,000 have died in the fighting, while more than 3 million refugees have fled the country.