The Center for Reconciliation in Syria which is run by Russia's Defense Ministry made the announcement, saying the evacuation took place in the town of Hammouriyeh, Interfax news agency reported.
Since humanitarian corridors were set up, more than 68,000 people have left Eastern Ghouta, the center added.
Russia has set up the passageways with Syria’s help to contribute to a United Nations Security Council resolution, which came into force last month mandating a ceasefire in the Arab country.
Syria and Russia have cornered foreign-backed militants in the countryside as part of their campaign to liberate civilians holed up there and end militant attacks from the suburb on Damascus.
During their advances in the area, Syrian forces have uncovered workshops used to make chemical weapons. The Syrian military has also intercepted several arms and ammunition cargoes heading to Eastern Ghouta.
One man, who had fled the suburb to the al-Duweir camp near Damascus on Saturday, said a lot of children suffer from malnutrition because militants are stealing the aid.
On Friday, civilians fleeing through the Hush Nasri corridor described in an interview with AFP news agency how militants were preventing them from leaving the area and using them as human shields.