State news agency SANA said the first blast was caused by a car bomb that detonated at a bus station near the shrine.
It said two suicide bombers then detonated their explosive belts when people gathered at the scene.
An AFP photographer at the scene said the blasts caused massive damage, shattering windows and ripping a huge crater in the road.
Smoke rose from the twisted carcasses of more than a dozen cars and a bus damaged in the blasts, as ambulances ferried away the wounded and firefighters worked to put out blazes started by the bombings.
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It has continued to attract pilgrims from Syria and beyond, particularly Shiites from Iran, Lebanon, and Iraq, throughout the war, and has been targeted in previous bomb attacks.
The Islamic State group claimed responsibility for bombings near the revered Shiite shrine.
In a statement circulated on social media, the jihadist group said two of its members had detonated suicide bombs near the Sayyida Zeinab shrine.
"Two soldiers of the caliphate carried out martyrdom operations in a den of the infidels in the Sayyida Zeinab area, killing nearly 50 and injuring around 120," the group said.
Also that month, a blast ripped through a bus carrying Lebanese Shiite pilgrims headed to Sayyida Zeinab, killing at least nine people, in an attack claimed by Al-Qaeda affiliate Al-Nusra Front.
The area around the shrine is heavily secured with regime checkpoints set up hundreds of metres away to prevent vehicles from getting close to Sayyida Zeinab.
The Britain-based monitor said 47 people were killed in the blasts, including a car bomb that targeted a checkpoint, and included non-Syrian Shiite militants without specifying their nationalities.