The FSB said those held included citizens of Russia and ex-Soviet Central Asia who were "preparing terror attacks with the use of homemade explosives on Moscow's transport infrastructure."
"As a result of searches at the detainees' places of residence a laboratory for making explosives was discovered and a ready-made explosive device," the agency said in a statement.
The alleged terror cell was directed by IS leadership in Syria and the suspects planned to flee there after the planned attacks to fight for the extremist group, it added.
Authorities have attributed the attack to 22-year-old Kyrgyzstan-born Russian national Akbarjon Djalilov and arrested 11 of his alleged accomplices.
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A lawyer for two brothers Abror and Akram Azimov -- accused of playing key roles in organising the attack -- told Russian news agencies Thursday that they had officially been charged with terrorism.
The Imam Shamil Battalion, a group suspected of links to Al-Qaeda, claimed responsibility for the bombing, US monitor SITE Intelligence Group said last month.
Islamic State jihadists have repeatedly threatened to strike Russia over Moscow's intervention in Syria in support of leader Bashar al-Assad.
Russia will next month be hosting the Confederations Cup football tournament, a warm-up event for next year's World Cup.
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