Rebels have launched several mortar and rocket attacks nto the centre of the Syrian capital on Sunday, where many embassies and senior Syrian officials are based.
The Russian mission was damaged in February when a car bomb exploded nearby on a busy Damascus highway, killing 50 people, Al Jazeera reported.
No one was wounded at the embassy, but that blast blew out windows in the building, Russian officials said.
The embassy attack comes on the same day that Russia criticised what it said were Western attempts to use a Syrian chemical arms disarmament deal to seek a UN resolution threatening force against President Bashar al-Assad's government.
"They see in the US-Russian deal not a chance to save the planet from significant quantities of chemical weapons in Syria, but as a chance to do what Russia and China will not allow, namely to push through a resolution involving [the threat of] force against the regime and shielding the opposition," Interfax news agency cited Sergey Lavrov, foreign minister, as saying.
Lavrov also said Russia, which has used its veto to block Western efforts to use the UN Security Council's clout to pressure Assad's government, was ready to send troops to Syria to ensure the safety of UN chemical weapons inspectors.