Photo credit: AFP/Baraa Al-Habibi
The explosions triggered widespread panic and smoke was seen coming from the embassy compound, according to a report. Moments before, demonstrators had been waving Russian flags at the embassy and holding up photographs of President Vladimir Putin, witnesses said.
A BBC Arabic correspondent in Damascus said that some people have been injured, but the number of casualties hasn't been revealed.
Russian Foreign Minister Sergei Lavrov described the shelling as "a terrorist act" and said the attackers were trying to "intimidate those fighting Islamic State".
The Syrian Observatory for Human Rights said the origin of the shells was the eastern part of Damascus.
Rebel forces based in the suburbs of Damascus have previously targeted the embassy. Last month, Russia demanded "concrete action" after a missile struck the embassy compound.