An Associated Press reporter was outside the embassy when the first shell slammed into the compound in central Damascus and smoke billowed from inside.
As people started running away, another shell hit the area. No one was harmed in the shelling.
Russian Foreign Minister Sergey Lavrov condemned the attack, saying "this is obviously a terrorist act intended to, probably, frighten supporters of the war against terror and to not allow them to prevail in the fight with extremism."
Rebels in the capital's suburbs have targeted the embassy in the past, and it was not clear if today's attack targeted the rally.
Insurgents have vowed to fight Russian forces after Moscow began launching airstrikes in Syria late last month. Russia has been one of Assad's strongest supporters since the start of the uprising in 2011.
Before the shelling, the demonstrators had gathered outside the embassy carrying posters showing Assad and Russian President Vladimir Putin, and waved the two countries' flags. Some held placards that read: "Thanks Russia" and "Syria and Russia are together to fight terrorism."
"President Putin's stances were absolutely positive for Syria," said 39-year-old civil servant Nizar Maqsoud. "All the West stood against us. Only Russia backed us . We are all here to thank Russia and President Putin," said Osama Salal, an 18-year-old student.
Russia began launching airstrikes in Syria on Sept. 30, allowing Syrian government forces to launch a multi-pronged ground assault.
