"Russia views such actions as an intentional provocation aimed at inflaming tensions in Russian-British relations," the foreign ministry said in a statement on its website.
Anthony Brenton, the UK ambassador, who was earlier summoned to the foreign ministry, said the British Council would continue to operate in Russia.
He warned that any Russian action against it "would be a breach of international law".
Jonah Hull, Al Jazeera's correspondent in Moscow, said: "The foreign ministry has all but admitted that this is part and parcel of its retaliatory measures last year against the British decision to expell Russian diplomats in London.
"They did say at the time they would consider extending their retaliation to include scientific and cultural ties."
British officials say the Russian move against the British Council is linked to the dispute over Litvinenko's murder by radiation poisoning in London in 2006.
Britain named Andrei Lugovoy, a former KGB bodyguard, as its suspect in Litvinenko's murder and in July expelled four Russian diplomats from the UK over Moscow's refusal to extradite Lugovoy.
Russia expelled four British diplomats in response.
James Kennedy, the head of the British Council in Russia, told the Reuters news agency that Moscow had made the dispute a political one.
"We haven't made this link [to the Litvinenko case], that link has been made by the Russian authorities," Kennedy told Reuters when asked about a connection.
The Kremlin says it ordered the two British Council offices closed because of long-standing concerns over their legal status.
It says the British Council is not in line with Russian law as its offices operate as separate entities from the British embassy.
The offices, which promote British culture abroad and arrange educational exchanges, have also been the subject of tax investigations.