There is no evidence the detainees, who are citizens of Central Asian countries, are in any way linked to Monday's bomb attack on a St Petersburg metro train, Russia's state investigative committee said in a statement.
The arrests were carried out jointly with officers of regional FSB and Ministry of Internal Affairs directorates, as well as special National Guard subdivisions.
The committee said that their homes were being searched and extremist literature had been confiscated.
The statement said the authorities had not yet decided whether to press charges against the detainees.
"Russia's Investigative Committee will thoroughly check all the ties and the contacts of the persons detained but (right now) the investigation has no data on the detainees' link and acquaintance with the perpetrator of the St. Petersburg attack", it said.
The remains of Akbarzhon Dzhalilov, 22, were recovered from the scene of the bombing, Russian authorities said on Tuesday.
After the attack, several Russian politicians have called for ending the moratorium on capital punishment.
Jalilov's parents, who live in the southern Kyrgyz city of Osh, were questioned there by Kyrgyz authorities on April 4 and were then flown to St. Petersburg.
A woman believed to be Dzhalilov's mother reportedly told a Russian TV reporter that she did not believe her son was the bomber.
Islamic State - which has fighters from ex-Soviet Central Asia among its ranks - has repeatedly threatened to attack Russian Federation in revenge for Moscow's backing of Syrian leader Bashar al Assad.
"We see that, unfortunately, the situation is not improving", he said.
"We do know that each of our countries, nearly every country, is a potential target of a terrorist attack", he said.
Moreover, the identities of all the victims of the St. Petersburg attack have been determined, Petrenko said.
"Once again, we have to unite ourselves and take tough measures [on combatting terrorism]", he said.