State news agency SANA had earlier reported 30 people killed in the three blasts, which it said were caused by a car bomb and two suicide bombers, AFP reports.
Syrian Observatory for Human Rights, a Britain-based group close to Syria's foreign-backed opposition, had initially reported eight deaths in the blasts.
Syria's television carried a breaking news alert reporting "two terrorist blasts, one of them a car bomb, followed by a suicide bomber... in the area of Sayyida Zeinab."
The Sayyida Zeinab mosque contains the grave of a granddaughter of the Prophet Mohammed (PBUH) and is particularly revered as a pilgrimage site by Muslims.
It has been targeted before, including in February 2015, when two suicide attacks killed four people and wounded 13 at a checkpoint near the shrine.
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.
