Syria: Twin bombings rock Damascus suburb Sayyida Zeinab
Some 13 other people were wounded in the blasts, which were caused by a suicide bomber and a car bomb.
The suburb of Sayyida Zeinab, some 10km (six miles) south of central Damascus, has been a frequent target of attacks.
Two bombings earlier this year - both claimed by the so-called Islamic State - killed more than 150 people.
The first blast, by an attacker wearing an explosives belt, took place at the entrance of to the suburb and the second car bomb attack detonated in al-Teen street, not far from the shrine, Sana news agency said.
The golden-domed Sayyida Zeinab shrine contains the grave of one of the Prophet Muhammad's grand-daughters, and continues to draw many Shia pilgrims despite the civil war.
Shia fighters from around the region have joined the conflict in Syria on the grounds that they wish to protect the shrine from the civil war, observers say.
The Lebanese Shia movement Hezbollah has cited it as a key reason that it chose to fight on the side of Syrian President Bashar al-Assad.
But this has made this suburb a prime target for the government's enemies, including the Sunni jihadis of IS, the BBC's Alan Johnston says.
More than 250,000 people have died and 11 million have fled their homes in more than five years of civil war in Syria.
Source: bbc.com