Syrian state TV said the suicide bomber detonated his explosives-packed vehicle at a military checkpoint at the entrance to the Sayyida Zeinab suburb. Syria's Al-Ikhbariya TV station showed footage of a slight depression on a road near a checkpoint where the bomb was said to have gone off. The wreckage had already been removed.
Al-Manar TV, run by Lebanon's Hezbollah militant group, said eight people were killed in the blast. The Shiite militants have a heavy presence in the suburb. The Syrian Observatory for Human Rights, an activist-run monitoring group, gave the same toll. Syrian state TV said five people were killed and 20 wounded.
Allies of the embattled Damascus government have mobilized Shiite fighters from Iran, Iraq and Lebanon to fight on the side of President Bashar Assad's forces on the grounds of defending the shrine and preserving the country's religious plurality.
A previous bombing in the Sayyida Zeinab suburb, claimed by the Islamic State group, killed some 130 people in February.
The Syrian uprising began with mostly peaceful protests in 2011, but a brutal government crackdown and the rise of an armed insurgency eventually plunged the country into a full-blown civil war.