The shrine, which is highly revered by Shia Muslims, has been targeted before, most recently in February last year.
The attacks came as delegates from the Syrian government and opposition groups gathered in Geneva for tentative United Nations-sponsored peace talks. The main opposition group backed down from its threat to boycott the talks, but said the Syrian government must meet key demands if negotiations are to start.
Syrian state media said that the blasts near Sayyida Zeinab yesterday were caused by a car bomb and two suicide bombers. TV footage showed burning buildings and destroyed cars.
The shrine contains the grave of one of the Prophet Muhammad’s grand-daughters. It continues to draw many Shia pilgrims, despite the civil war in Syria.
Shia fighters from around the region have joined the conflict on the grounds that they wish to protect the shrine from the civil war. The Lebanese Shia movement Hezbollah has cited it as a key reason that it chose to fight on the side of president Bashar al-Assad.
More than 250,000 people have died and 11 million have fled their homes in almost five years of civil war in Syria. The violence has also been the biggest driver behind Europe’s migration crisis.
In Geneva, the delegation of the Saudi-backed opposition group the High Negotiations Committee (HNC) met UN envoy Staffan de Mistura yesterday.
Mr Mistura described the talks as “a good start” and said he was “optimistic”.
HNC spokesman Salim Muslet said government attacks on civilians must stop.
Earlier, Mr Muslet had said that they stood by their demand for an end to air strikes and blockades before they would negotiate with the Syrian government.
The HNC finally agreed late on Friday that it would travel to Geneva – hours after the Syrian government delegation had arrived and held preliminary talks with Mr Mistura.
The so-called proximity talks are expected to last about six months, with delegations sitting in separate rooms and UN officials shuttling between the groups.
UN secretary-general Ban Ki-moon called on all sides to put the interests of Syrians above their own.
He said: “Children and women in particular have borne the brunt of this fighting and it is time now to see the end of the fighting and other human rights abuses that have dominated the war.”