The last big attack in Moscow was a suicide bombing that killed 37 people at Domodedovo Airport in January 2011, but since then, Doku Umarov, the man who claimed responsibility for it, says he has ordered a halt to attacks on civilians in Russia.
Umarov is the leader of the outlawed Caucasus Emirate and Russia’s most-wanted insurgent.
Kremlin spokesman Dmitry Peskov said Putin had been kept informed as the security services surrounded the apartment bloc in Orekhovo-Zuyevo.
It was not immediately clear where the suspects came from.
Russia has voiced concerns Islamist violence could spread northward with the withdrawal of most NATO-led combat troops from Afghanistan by the end of next year.
Russian media cited a name, provided by a source in the law enforcement agencies, which suggested the man in detention was from the North Caucasus.
State-run media have been giving increasing prominence to Moscow’s fight against insurgents as the Olympics approach.
Making the most of any successes against Islamists could help Putin rebuild support after 2011 saw the biggest demonstrations against him in more than a decade of power, although protests have dwindled since then.
In another apparent success for security forces, investigators on Tuesday said they had killed Umarov’s right-hand man, Dzhamaleil Mutaliyev, who the committee says masterminded a bombing in 2010 that killed 18 people.