There have been no casualties in the attack, the ministry said, noting that the building sustained a certain level of damage.
Two mortar rounds fell on the territory of the Russian embassy with two more hitting close to the mission's perimeter, according to the statement released by the ministry.
"We strongly condemn terrorist attacks on Russian diplomatic mission in Damascus," the statement read. "We'd like to reiterate once again that Russia has drawn attention on multiple occasions to barbaric nature of the bombardments, which terrorists regularly carry out against the residential quarters in Damascus and other populated Syrian cities. Every day, civilians, women and children become the victims of these attacks."
Russia hopes that the Western countries in the United Nations Security Council will comment on the attack, the statement said.
Later, Moscow expressed regret that some UN Security Council members refused to qualify attacks on the Russian embassy in Damascus as terrorist acts.
"We regret to say that some members of the Security Council have again refused to consider the Russian draft under a far-fetched pretext of the lack of evidence on the terrorist nature of the attacks," the statement said on Tuesday. "It was proposed to delete all important provisions of the draft. In these circumstances, the Russian delegation found it pointless to continue work on this document."
Moscow has been conducting a counter-terrorist campaign in Syria since September 30, 2015, at President Bashar Assad's request.
The civil war in Syria has been lasting for around six years with government troops fighting against numerous opposition factions and terror organizations such as al-Nusra Front and Daesh, outlawed in Russia.
