David Khakim was led away by police after holding up a placard saying "Freedom for Yevgeny Vitishko" beside a sign depicting the Olympic Games logo near the city administration's offices.
He was later sentenced by a Sochi court to 30 hours community service, his lawyer Alexander Popkov said, adding that Khakim would appeal against the decision.
Protests in Sochi are confined to a specially designated area during the Games and must be agreed with the authorities.
President Vladimir Putin has tried to keep a lid on protests during the Sochi Winter Olympics to prevent them undermining his efforts to use the Games to show how far Russia has come since the Soviet era.
A regional court last week rejected Vitishko's appeal against a three-year jail sentence on charges of damaging the regional governor's property, which he denies.
Vitishko's supporters say he is being punished for publicising environmental problems caused by the Games construction projects and say the case was politically motivated.
Vitishko has begun a hunger strike in protest at his treatment, said his organisation Environmental Watch on the North Caucasus.
Putin has been criticised over the high cost of the Games and his stance on gay rights as well as over the damage which activists say has been done to the local environment. He has dismissed the criticism.
(Editing by Mitch Phillips)
