Reports say nearly 20 other people were injured in the mortar attack on Thursday.
The holy shrine is located in the southern suburbs of Damascus.
The site also came under a terrorist attack on July 19. Takfiris fired several mortar shells at the shrine, killing a custodian.
Hazrat Zaynab was the daughter of the first Imam of Shia Muslims, Imam Ali (peace be upon him) and the granddaughter of Prophet Muhammad (peace be upon him).
The attack comes as the Syrian people are celebrating Eid al-Fitr, which marks the end of the holy month of Ramadan.
Syrian President Bashar al-Assad performed Eid al-Fitr prayer at the Anas Bin Malek Mosque in the capital on Thursday, alongside the Syrian Grand Mufti Ahmed Hassun.
Turmoil has gripped Syria for more than two years now.
According to reports, Western powers and their regional allies – especially Qatar, Saudi Arabia, and Turkey – are supporting the militants operating inside Syria.
The United Nations says more than 100,000 people have been killed and a total of 7.8 million displaced due to the foreign-backed militancy in Syria.
Over 1.8 million of the displaced Syrians are living in neighboring countries, mainly in Iraq, Jordan and Lebanon.