"Sbeineh was one of the most important rebel positions on Damascus' outskirts. Rebels in southern Damascus have now had practically all their supply routes cut off," said Syrian Observatory for Human Rights director Rami Abdel Rahman.
State television also reported the takeover.
"Our brave army has taken control of... the Sbeineh (area)... and (the nearby village) of Ghazalah in Damascus province after crushing the last terrorist positions there," said the broadcaster, using the regime's terminology to refer to rebels.
The takeover of Sbeineh, a rear base for rebels in southern Damascus, comes a year into a suffocating army siege of the town.
It also comes nine days into an intense campaign aimed at cutting off one of the main rebel supply lines into southern Damascus, said the Britain-based Observatory.
"The army was backed by fighters from Hezbollah, the pro-regime paramilitary National Defence Force as well as Syrian and non-Syrian Shiite fighters from the Abul Fadl al-Abbas brigade," Abdel Rahman added.
"There are fears for the lives of civilians in Sbeineh. Experience tells us that the army may well execute civilians and put the blame on rebels," he said.
The takeover of Sbeineh comes weeks after the fall from rebel hands of nearby Husseiniyeh, Ziabiyeh and Bweida.
An activist based east of Damascus said the army "is definitely advancing. It is because the areas have been under siege for such a long time. It's natural."
Abdel Rahman also attributed "divisions among the rebels" for the army's recent advances.
He said both sides suffered heavy losses in the fighting, and that "the fight south of Damascus is more sectarian than elsewhere."
The burial site of Sayyida Zeinab, granddaughter of the Muslim prophet Mohammed, is an important Shiite shrine located in southeastern Damascus.
The proximity of the shrine to several areas under the control of mainly Sunni rebels has attracted well-trained Shiite fighters from neighbouring countries to join the loyalists.
Assad's regime has waged an intense campaign for months to try to secure the capital by crushing rebel enclaves nearby.