The seven were arrested for "public disorder" but four were quickly released without charge, local agencies quoted Moscow police as saying.
Several of those arrested were holding banners in support of a jailed protester, according to OVD-Info, an organisation which specialises in monitoring rallies.
Elsewhere, more than 2,000 people gathered to mark the fifth anniversary of anti-government demos that erupted into violence.
Some 30 people were arrested at the time of that demonstration, which took place in central Moscow on the eve of Putin's swearing-in ceremony.
Several of those arrested in 2012 later received jail terms of up to three and a half years in sentences fiercely criticised by human rights groups.
"Today five years ago, police provoked riots on Bolotnaya Square and several dozen people were arrested under false pretences," said 37-year-old protester Alexei.
Another demonstrator, who gave her name as Daria, said: "We're 18 and we have lived our entire lives with Vladimir Putin as president. We are tired of this situation."