The FSB security service, the successor to the KGB, said it had detained 10 people originating from Central Asia who were "planning to commit a series of high-profile acts of sabotage and terror in Moscow and Saint Petersburg".
It said the suspects, detained in an operation in conjunction with the ex-Soviet Central Asian states of Tajikistan and Kyrgyzstan, had testified to contacts with IS leaders.
It said the group were suspected of plotting to murder civilians in busy public places using automatic weapons and powerful homemade explosive devices.
During raids on Saturday, the FSB said it confiscated four homemade bombs as well as trigger devices, guns, ammunition and communications equipment.
The FSB periodically reports on foiling major attacks on Russia and in annexed Crimea, while giving few details.
Membership of a "terrorist organisation" is punishable by 10-20 years in prison under Russian law while leading one is punishable by up to life in jail.
Impoverished majority-Muslim Tajikistan and Kyrgyzstan both say they are battling Islamist extremism.
Tajikistan says that up to 1,000 of its nationals are fighting with radical groups in Syria and Iraq, while Kyrgyzstan says that some 500 of its citizens have gone to fight alongside jihadists.
